Why would professors pay to publish in a good journal?
Note: as pointed out by Pieter Naaijkens, PRL indeed has a publication fee, making most of the original answer incorrect. I've rewritten the answer as a result.

When one pays a publication fee that isn't open access, one is effectively paying the publisher to distribute the paper. Most (subscription) publishers and journals are quite content to distribute the paper for free - a publication fee is bound to reduce submissions, which the journal needs to function. In this sense, Physical Review Letters is very unusual. 

I have no knowledge of the internals of PRL, but I will guess that they have more expensive costs than normal because of the numerous full-time PhD scientists they have on their journal staff. They are presumably offsetting some of the costs by charging a publication fee. Cynically, they're able to get away with it because 1) APS is perceived positively by people (even though their open access APCs are on the high end of the market rate) and 2) they're such an important journal (note other APS journals don't have such a fee).

Why would professors pay the publication fee? I imagine the most important reason is because they really want the prestige that comes with publishing in PRL. Other lesser factors could be they like the review process, and because PRL as one of the premier journals in physics has a very wide distribution.