Addendum: One useful thing I've found about reimbursing (note: NOT splitting, which is what you were talking about) some other bills down to the penny is that it makes it much easier to search for them afterward if you want to figure out whether you remembered to pay for them. Like if you buy someone dinner and they insist on paying, don't round $10.49 down to $10 or up to $11. Because then you have different numbers showing up on different accounts (credit card statement vs. bank statement vs. Venmo/whatever) and it makes it harder to see if you remembered to pay for it or not.

Aside from the social awkwardness/pettiness, it doesn't really work for typical bill splitting anyway, since it's not like they would remember what amount to search for, given that usually the person paying has the only receipt. Where this method really shines is when someone is reimbursing you in a bulk/lump payment -- in that case it's far more valuable to know that the actual amount was $304.01 instead of just something rounded to $300, since then it'll be a lot more work to figure out if that payment included a $6.23 item or another $7.98 item or whatever.