It's not about the money (a penny would be totally inappropriate in that case: that's an insulting offering if we're talking about money as money). I think it's mostly about having a simple physical object you can anchor the energetic offering to. Just dumping it on the tree seems rude, the same way that dumping it on someone else would be: by transferring the offered energy to a secondary object nearby, it's like sticking it out on a plate: the tree can use it or not.
I've got the same sort of grumpiness about penny offerings, as they seem to usually be done in Pagandom, as Grymdycche (which includes what you said about them being insultingly small), and do strongly prefer making energy offerings. I haven't had any problems with just giving it directly - might be an animist thing; it's all part of the ongoing negotiatory conversation, for me - but you've given me another way to look at the whole thing. Good for teaching students (who may not be animists, or may not have facility conversing with things, or whatever); good for times when I have trouble having a clear convo.
It makes more sense to the "flavor" of my path to go with hair; also, I have some idea (not sure where I got it and know nothing of details, so it might be BS) that not everything pennies leech is beneficial to all plants. Which could be true of my hair, too, I suppose, but OTOH I shed several strands a day anyway, so it's out there in any case.
New tool for the toolbox!
Sunflower