I don't do full 5 gallon batches for some of the reasons you are stating. I'd like to run a lot of batches to gain experience and to try different things. I've got way more beer than I can use running 4 gallon batches that end up with about 3 gallons of finished beer.
I use a 5 gallon igloo cooler and a BIAB bag in it. I can keep my mash temperature steady this way, do step mashes if I want to, and its a little less messy separating the wort from the grains. When I did BIAB in my pot I couldn't help but spill wort all over my smooth top range when I pulled the bag out. I had to clean that up before starting my boil.
I also had trouble maintaining my mash temp using the BIAB method in a pot instead of a cooler.
I do 4 gallon batches with my setup, so I have to batch sparge, but If you were doing 2 gallon batches the whole boil volume would fit no problem.
The only problem with the 2 gallon batches is it doesn't really go any faster than a 3 or 4 gallon batch using a kitchen stove.
You might get faster ramp times for your strike, sparge and boil, but you still are putting in
significant time for not that much beer.
I have 3, 5 and 6 gallon carboys I use for secondary conditioning and dry hopping, I've found that too much headspace in the carboy can lead to moldy looking growth on the top of the beer, unless you can keep it cold. So I run a 4 gallon batch in a plastic bucket primary, and rack off to a 3 gallon carboy secondary. If there are a few quarts of beer that don't fit in the carboy, I use 1/2 gallon jug, put these "dregs" in the fridge and blend this young uncarbonated beer with something else and drink it within a few days.
You can use 1 gallon glass jugs for fermenting, but by the time you settle the yeast you are only going to have 3 quarts of beer.
Cooling 1-2 gallon batches will be easier, just use your kitchen sink and some ice.
So there's pluses and minuses with smaller batch brewing. I've kind of found a middle ground that works for me. Unless I can find a need for 10 gallons of beer at one time, I'll
never go to that large of a setup.