This is the sort of argument that causes people to reject vaccination.

1. "a smaller but still relatively high probability of hospitalization."

The risk of hospitalization for COVID is (in the UK, other countries are comparable) something like 0.1% per week for the 65-75 age range [1]. It is much lower for younger people. Ignoring the actual probability of getting infected is not legitimate - people care about overall outcomes. Claiming this is a "relatively high probability" is the sort of false claim that creates resistance to vaccination, because it makes the people promoting vaccination look mis-informed. Especially when they claim to be more rational and have better information than the people they're criticizing, this is guaranteed to piss people off and make them double down on their position. After all, someone who tried to convince them they were wrong just demonstrated an incorrect understanding of risks, and vaccination vs infection is all about marginal risks.

2. "A symptomatic COVID infection has a fairly high probability of a long haul case"

Long COVID isn't even a definable thing, so talking about it will immediately reduce your credibility with those who don't want to take a vaccine. You really have no idea what the probability is given that long COVID isn't a real disease, in the sense of having a defined set of diagnosable symptoms.

Injuries from taking the vaccine on the other hand are definable. Most countries have databases with entries describing those injuries, but they are incomplete so it's hard to know the full risk. Most pre-COVID studies suggest the under-reporting rate is anywhere from 10x to 100x, so the true numbers are certainly quite high, especially as under-reporting for COVID vaccines is clearly much higher: lots of people claim the vaccine made them sick for a day or three, but don't report this. So people who talk about the risk of long COVID but never talk about the risk of long vaccine look biased and irrational (i.e. not doing a cost/benefit analysis).

3. "It should be painfully clear that with a high infection rate the hospitalization rate is high enough to flood hospitals"

There are quite a few countries have got through prior waves in which nobody was vaccinated without hospitals being overloaded. Switzerland for example publishes long term data on hospital capacity. As you can see [2], at no point did the country run out of beds or even come close. In fact ICU beds have been decommissioned over the past year because there were too many, and regular hospital beds were never more than 10% COVID occupied. Therefore, this is not painfully clear, especially as you're using vague terms like "flood" and "high".

4. "Waiting to gain immunity to COVID through natural exposure has a high chance of a long haul condition, hospitalization, and death"

The COVID IFR estimates published by the WHO is ~0.2%. This is not "a high chance ... of death".

5. "There's no dilemma about vaccines for anyone being rational"

You have just demonstrated that you don't understand the actual risk levels involved with COVID, so it would be wise to refrain from criticizing other people's rationality.

[1] https://www.ons.gov.uk/peoplepopulationandcommunity/healthan...

[2] https://www.covid19.admin.ch/en/hosp-capacity/icu