There are two reasons why you should absolutely boil your water instead of purifying with the sun on a backpacking trip.

1. Fuel is light, water is heavy.

A liter of water weighs roughly 2.2 pounds. That is not including the weight of the containers holding the water. Assuming a person is hiking from 8AM until 12PM, and drinking approximately 1 liter of water an hour, they will consume approximately 4 liters of water on their hike. Then, they will likely need at least 3 liters of water at camp for cooking, cleaning, and drinking (I use about 2 liters on average in camp for solo trips but I hike until sundown so I'm adding some extra drinking water for sitting in camp during the hottest part of the day). So, using a fairly conservative water estimate, a hiker like you described would need about 7 liters of water in a day, which would weight about 15.4 pounds plus the weight of containers.

Using the sunlight method you are advocating, the person will need to carry all of that weight during their hike. Even worse, the sun is unreliable. On cloudy days, it could take up to 48 hours to purify the water. So the hiker would want to carry 2 days worth of water (14 liters at 30.8 pounds plus container weight) to ensure a steady supply unless absolutely guaranteed a perfectly sunny weather window (which is rarely a guarantee that can be reasonably made). Adding in the last piece, container weight, makes the situation worse. An average empty 1 liter SmartWater bottle (a good analog for the coke bottles you mentioned and a commonly used option by the backpacker community) weighs 1.3 ounces. So to carry 14 liters of water, you will need 14 bottles, weighting 18.2 ounces or 1.13 pounds. The total weight of water carried for a leisurely backpacking trip using your proposed method would be a shade under 32 pounds.

Now to the boiling method. Using a modern backpacking canister stove, you can boil a liter of water with about 15-20 grams of fuel depending on elevation, temperature, and wind conditions. Lets say 20 grams to be conservative. So to boil that 2 day supply of 14 liters of water, you would need to carry 280 grams worth of fuel, which is about 0.6 pounds. This is not including the weight of the fuel container because I am assuming the hiker is already bringing a canister stove for other purposes, as most backpackers do. Other stove types such as alcohol and esbit weigh even less. By bringing this 0.6 pounds of fuel, you no longer need to carry most of the water during your hike. The majority of long distance hikes in the US and around the world have regular sources of water along the route. Most hikers will only carry 1-2 liters of water during the day, filling up and purifying along the route. Then they top off shortly before making camp for the night. So now, with a faster purification method, the hiker only needs to carry 2 liters of water, which weighs 4.6 pounds with containers. Add the fuel weight and the hiker will be carrying 5.2 pounds total for their water system, a weight savings of 26.4 pounds over your method. Even adding a few more liters of water for more water scarce routes (such as the southern portion of the Pacific Crest Trail) will result in double digit weight savings.

When most backpackers these days are aiming to keep their total pack weight under 30 pounds for most trips, this weight savings is a HUGE deal.

2. Boiling is reliable, sunlight is not.

When you boil water, you can be reasonable assured that your water has been properly purified. Sunlight purifying is not so simple. As you said in your first post, the sunlight method requires variable amounts of time based on weather conditions. This causes scheduling problems on a backpacking trip because you need to wait longer for your water to be drinkable in bad weather. As I mentioned above, this forces the hiker to carry more water to account for bad weather.

But even worse, there is no concrete sign with sunlight purifying that your water is ready to drink. Assuming you can figure out how to strap 14 liters of water to the outside of your pack while you are walking so that they all get equal sun exposure (which is probably not possible) and it is a sunny day, you could hope that the water would be ready to drink in 6 hours. And maybe it is. Or maybe you were walking through shadier paths than you realized, or your shadow from your hiking hat blocked some sunlight, or 1 of 100 other things happened to prevent your water from being exposed to the sun properly. Then the water is not ready in 6 hours, but you drink it thinking it is. Now you are vulnerable to all the same problems you would be if you didn't purify at all.

If you boil your water for 3 minutes, it is always pure. If you use sunlight purifying, you are playing a dangerous lottery while out in the wilderness far from medical assistance.

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Finally, a note about using sunlight purifying as an emergency method in the backcountry. You are right that it could potentially be used in such a way. However, this would very rarely be necessary or practical. Most backpackers brings 2-3 methods of water filtration with them. Usually those methods are a filter/steripen/etc, filtration tablets as a backup (because they weigh almost nothing and work in less than 30 minutes), and their stove to boil water as a last resort. The situation where you are in an emergency situation and all 3 of your purification methods are inaccessible would be extremely rare. The only instance I could think of would be if you lost your pack, maps, the trail, and had no idea where you were going but were otherwise uninjured (so you could handle trips to a water source and carry large amounts of water to sunny purifying locations) and had access to containers to hold large amounts of water. Then maybe, hunkering down and purifying water with sunlight would be the right move while waiting for rescue. However, the odds of this happening are extremely rare. I have hiked thousands (probably tens of thousands) of miles in my life in very remote places. I have never had such a situation happen to me or anyone else I know who is a backcountry enthusiast. You should absolutely be more prepared than that!

In most instances, an emergency situation involves you being lost of injured. If you are lost, hunker down, make yourself visible, activate your beacon (which you should have in particularly remote areas away from trafficked trails) and wait for help while you use your normal filtration methods (1 of 3 at least should work). Rescue should come within a day or 2. Same thing if you are slightly injured and don't think you can walk out under your own power. Or if you can walk, just get out as fast as you can. If you are severely injured and lost your pack (maybe from a severe fall or bear attack), make it to a water source if possible and just drink the water. If you don't get help within a day or 2, you are probably dead anyway from your injuries. The most important thing is to stay hydrated and make yourself visible, not sit around waiting for your water to purify for 6-48 hours. I'd rather be found alive and deal with Giardia for a month than be found dead with some nice clean water next to me.

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TLDR: PLEASE PLEASE PLEASE don't rely on sunlight as a method of backcountry water purification. It is well suited for purifying water cheaply in water troubled villages, but uniquely unsuitable for backpacking. Always learn proper backpacking techniques for water filtration (along with first aid, navigation, camping, etc), know your physical limits, thoroughly research your route, and have the right gear before setting out into the backcountry. My mountain community buried 9 people last year who died in the backcountry. Most of those deaths were caused by inexperience and were completely preventable. Please don't add to that number.