Regarding tire removal, I recently did it like three times in a single week. It was like 15 minutes in sweat and finger pain every time. To get an idea of what one can achieve, can you remove a tire without tools with fat tires only or even thin road tires? Mine were thin, 23mm (less than an inch). By the way, in this instance, it wasn't a beater but a high-end 1970s bike.
Thanks for the advice, I'll look into it because it sounds like I'm missing something.
How difficult it is to remove or replace a tire really comes down to the tire/rim combinations. Different types and sizes of tires can make a big difference.
Some combinations can definitely be trickier to mount, but with the right it can usually be down without too much physical strain. Mechanics in the bike shop do it many, many times each day after all.
(For example, it should not take 5 minutes to replace a wheel. That should take about 10 seconds... I am genuinely curious what you spend your time doing over the 5 minutes and I am sure some practice / instruction could save you frustration. Likewise, even for a very tight tire you should be able to remove it quite quickly. A small tip I can give you for removing a tire is to make sure that the entire bead of the tire is unseated and sitting in the deepest part of the rim. This leaves a good amount of slack to pull the tire off. I usually am able to remove a tire without any tools, but a tire lever can make it even easier when used correctly.)
Certainly patching a tube adds to the time, I didn't include that in my 3-5min estimate. The usual practice is to pack an extra tube while out on a ride and patch the damaged tube later at home. Also worth noting there are modern patches that come with adhesive pre-applied that are very easy & quick to use, just peel and stick.
Cheers and good luck!