Retain control of your own reprint/anthology rights.
It is a giant bureaucratical pain in the ass to deal with publishers regarding reprint rights for anthologies. The permissions departments frequently 1) require insanely arcane request procedures, 2) willfully obscure the identity and location of the proper contact human(s), 3) ignore repeated written requests, and/or 4) charge ridiculously exhorbitant fees.*
The benefits for you, the poet, of signing over reprint/anthology rights to your publisher: hmm, none.
The benefits for you, the poet, of retaining those rights yourself: 1) you are able to grant (or deny) reprint rights yourself, which means 2) you will know when and where your work is being reprinted, and 3) your work will reach a wider audience, and/or 4) you will receive payment for your work instead of the press you signed the rights over to (& they probably didn't pay you for them anyway) if the requesting press's budget allows it. (Yeah, in the case of anthologies payment is usually just a complimentary copy, but still!)
And for goodness sake, if you become "famous" do appoint a literary executor who isn't reclusive, insane, or liable to vanish into thin air.
* For example: Say an anthology is collecting collaborative poems by American poets, ranging from 1940 to the present. Say the anthology contains more than 150 poems written by well over 200 contributors (since each poem has 2 or more authors). Say the press producing such an anthology is a small independent press with a budget to match and no nonprofit funding. Say they're hoping to break even, but not even really counting on it. Say the staff editor has been volunteering her time for the last year so she can finish this project. Say the anthology editors didn't run screaming in horror when they heard what their piddly advance would be. Say the contributor payment the press is offering for reprint rights is in complimentary copies. How many copies is that? How much does each copy cost to produce? How much does it cost to mail each copy of this 400+ pp. tome? Now . . . how in the f*ck do you expect said press to be able to afford $130 per poem in permissions fees? If you can answer these questions without losing your everloving mind, give me a shout.