career - How important are publications for undergrads?

I am (as always) speaking with regard to mathematics, not CS or or some other field:

Undergraduate publications are not viewed as a requirement, nor even necessarily a big plus, in a grad school application. (By cosmic coincidence* I have a stack of grad school applications to look at tomorrow, so if I change my mind on this I'll let you know.)

There is something to the idea that undergraduate papers are more prevalent now than they used to be. I think this is partly because the worldwide mathematical community is more connected and more collaborative now, so it is less critical to be in the right place at the right time in order to do undergraduate research.

The thing about undergraduate papers is that, unsurprisingly, they are most often not very good compared to papers written by more mathematically mature people. (Of course there are some exceptions, my favorite being Furstenberg's one paragraph Monthly article which gives a topological proof of the infinitude of the prime numbers. But even this, while brilliant, certainly does not represent his best work!) There's also the suspicion -- whether true or not -- that the behind the scenes advisor (who may not even deign to appear as a coauthor on undergraduate work) is likely to be the brains behind the operation.

I think it is a good thing to try to do some research as an undergraduate -- I did a summer REU at Indiana University, which was great -- but to realize that it doesn't matter too much whether it gets written up and/or formally published. Surely there should be a stage in one's mathematical training where one doesn't need to feel the pressure to publish!

*: Not really.