The fact that you have to go to the bank to get them (vs say from the ATM), also shows that you put thought and effort into the gift. So you way of saying "thank you for giving a shit" in itself rings more true, you gave a shit about thanking someone rather than an empty "hey thanks".
Regional credit union. Whether I've been broke (or not), they've never charged for denominational straps. I do often have to "order" twos (returning a week later).
Tipping with $2 bills was a "cool" thing oldsters would do, because the bills are a novelty but not actually that hard to get. They'd also give them for birthday money and such (I have a bunch in an envelope somewhere for that reason).
You're right that at this point you'd need to be giving out a lot of them each time for it to count for much. Dollars are worth so little that we're beyond "let's get rid of pennies" and approaching "WTF is the point of coins smaller than the quarter?"
[EDIT] That first bit comes off as harsher than I meant. I just mean that this was a more common thing years back, lots of folks of a certain generation (or couple of generations) did it, and at this point I can definitely see how giving out $2 bills, which was once novel (though when the eighth older person did it in a year, not so novel...) and also a decent amount of money, is getting into "yeah, thanks for the two whole quarters, grandpa, I'll be sure to buy a candy bar with them when I get several more" territory, thanks to inflation.
[EDIT EDIT] I'm struggling with internalizing new prices, too, incidentally. I've finally learned that when my kids get $10 it is not worth getting them excited about going to get a toy with it. They'll need, bare minimum, double that amount, and even then there won't be a lot of options after tax. There's almost nothing they can get with $10 but candy or shitty collectible (ahem, kiddy gambling) card crap.
At the risk of going too far OT, here's a story of how I did something different that wasn't expensive but was still seen fondly by all concerned.
So ~15 years ago our son had been invited to his best friend's birthday party. Unsurprisingly, the birthday boy had a list of electronic toys on his gift list, as had become tradition.
While my wife and I were out shopping for said gift, she located one of the electronic items. Probably a game cart for whatever was popular at the time.
Meanwhile, I had come across something that had stirred up fond memories of my own: a sleeping bag + flashlight (+ some other related item) combo. Woo :)
We decided to get both the game and the sleeping bag combo, just in case the latter wasn't well-received.
At the birthday party, I think literally every other gift was for his gaming system. Once he opened the sleeping bag gift, he, his mom, and at least a few of the other kids had a "wait - okay that's different and kinda cool" reaction.
Even if he never went camping with them, I hope he got many hours of use out of that sleeping bag and flashlight. I know I did with mine.