Yes, you could, like this: https://www.esmagazine.com/articles/102597-low-cost-direct-s...

I would say the best setup depends on your goals, e.g. "save as much money as I can" vs "be totally off-grid and self-sustaining" vs "have a superbly engineered system that I personally designed but nobody else can understand or maintain".

Starting from a finite roof area, you can install X modules. The higher-efficiency ones (meaning more power per square area) are more expensive. Then you have system efficiency losses from everything from DC/AC inversion (as you pointed out) to wiring to temperature to cloud cover to dust to sunlight angles, whatever. Ballpark, you can expect to get roughly 80% efficiency (meaning you can expect 80% of the array's nameplate output -- the sum of what your modules' wattage is listed as -- to be usable power that your loads can use). If you're going to throw batteries in there, you would lose a bit more efficiency, especially as time goes on.

Example 1: All you care about is hot water

If for some reason you don't care about the rest of your power draws in your house, you can fill your roof entirely with PV modules (generates electricity) or solar thermal collectors (sunlight heats a coolant, coolant gets pumped inside and a heat exchanger heats your water tank), then have the entirety of your production go towards your water heater. Excess heat beyond your temperature setpoint has to get shunted somewhere (so you don't boil yourself alive) and is generally wasted, unless you can heat exchange it with some other home heating system (radiant floor heating, for example). Otherwise you might just have one really hot utility room or dump the heat back outside. This is a super simple system, but you're essentially losing out on all the excess production.

Example 2: If you want to optimize payback by selling back to the grid

The most common residential PV systems are simple grid-tied ones where you generate power and buy/sell from/to the grid as needed. These days 300W+ modules are very common, so many households can generate more power on their roofs than they need, especially during the summer. Depending on your local electric utility and power buyback rate regulations and how they interact with time-of-use billing, it may make sense to either sell back to the grid all the time, or sometimes bank that excess production in a battery bank/electric car/supplemental heat for a water heater, etc. until you can sell back at a higher rate. It becomes a game of power arbitrage and you're basically a small power plant for the utility to buy from.

Example 3: You don't want to be connected to the grid at all

The math for this changes a bit because you're no longer concerned about time-of-use or selling back electricity, you probably just want the most days of autonomy you can get (i.e. how many cloudy days you can withstand before the lights go dark). That's a trickier formula involving your roof space, sum of your household average loads, your peak draws (do you need to run power tools or an electric stove/heater/air pump), the sunshine-days (average insolation) in your area, etc. From there you'd work backwards, figure out an appropriate battery bank size (due to chemistry, li-ion and lead-acid batteries have optimal depths of discharge you want to calculate for), maybe get the highest-efficiency modules you can find, etc.

Other examples: AC-coupled hybrid on/off grid systems (to survive power outages but also be able to sell to the grid), DC-direct households (like you can use DC appliances and lighting, such as those made for RVs, throughout your offgrid cabin), ground mounts to add additional PV modules if you have a lot of electric cars or whatever, tilt-mount axes (not as popular anymore because it's cheaper to just add modules), microinverters and power optimizers to maximize the per-module output on a curve... it can get super complicated if you really want it to.

But I'd caution against unnecessary overengineering.

If you go with a bog-standard grid-tied setup, not only will it be the cheapest (probably), you can more easily repair/replace components as they wear out in the future. Batteries have the most limited lifespan (10 years? maybe more if you use modern chemistry and manage it really well), followed by inverters (15-25 years?)... the modules themselves are probably going to outlast the rest of the system.

If you make something super complicated, it's going to be harder to find people who can maintain or replace it as it ages. Solar is not a especially high-margin business, so resellers and installers go in and out of business all the time, and if you have something really nonstandard, you'll have to pay extra for specialist engineers who can understand your particular setup vs any standard solar install crew.

But it's a cool field... have fun and sorry for being so longwinded, lol