The problem is those "just two minutes" add up time wise and cost wise. If you break it down on a trip by trip basis then it seems trivial as "it's only 40p a trip" (for example) but when you look at the cost as a whole over a longer period of time then those trivial amounts add up. Then you sound petty asking for a contribution on a weekly basis when it's such a small amount but if you wait a couple of months and then ask for £10 to cover the last couple of months costs then people get narked because you never said anything in the beginning.
Especially at the moment with the cost of living going up, as someone making barely over minimum wage who has had bills go up massively in the last few months, recently o have found I barely have £10 left a few days before payday more often than not so all those "just two minute" trips people are expected to absorb the cost of could literally be the difference between finishing the month in the red or in the black. I'm not about to share my financial situation with everyone I work/volunteer/interact with but as nice as a gift at Christmas is, it doesn't put fuel in the tank or help with the decision of whether to spend my last £10 on fuel to ferry other people around or groceries for DD and I, and I'm not about to say "Sorry Ethel, I can't take you to choir practice as I can't afford the fuel even though it's only an extra couple of miles to pick you up" because it's embarrassing to have to admit that.
Not only that but it's always easy to say "it's only a couple of minutes" but once resentment starts because what was once an occasional favour, or what was supposed to be short term support, turns into an expectation or a long term commitment then it is very hard to get out of that mindset. Even if someone is grateful for the lift it's the extra admin - if you can't go to a class (or just CBA one week) then you have to tell the other person so they can find other transport; you have to work round the expectation of picking up/dropping off someone else.
Sometimes giving lifts to someone very close is worse than someone where you have to detour. At least with a detour you can drop the person off and then decide whether you want to continue home or go back and do your grocery shopping, for example, but if they only live a minute or two away then you either have to drag them on your errands (and even if someone says "Oh it's fine, I don't mind!", I mind and I feel pressured to do things quickly) or instead of going venue > shopping> home you essentially have to go venue>home>shopping>home, so that "two minute" lift has cost you significantly more in time, cost an inconvenience (even if you don't do your shopping and just go straight home then it means you have to go another time which may not be convenient)