I like this idea, because I strongly feel that answers aren't self-deleted often enough.
The rule wouldn't even have to be onerous: set a threshold for total answers, and if 50% or more are not accepted and scored <= 0 then the user has to remedy that before posting more. Since answers can almost always be self-deleted (unlike questions), this offers a clear and easy path to grace for users looking to redeem themselves.
Obviously if they wish to edit their answers and wait for up-votes... or just leave... that's fine as well.
Ok, here are some stats:
User % Below Threshold Total Answers
----------------------------- ----------------- -------------
klox 100 34
Bharanikumar 100 35
jeeva 97.222222222222 36
Rajesh Jadhav 94.594594594594 37
Deepak 94.594594594594 37
sanders 94.444444444444 36
Phil Jackson 93.75 32
Patrick 91.304347826086 46
marc-andre menard 91.228070175438 57
4thSpace 91.176470588235 34
combi001 90 40
First thing that jumps out: these are users using answers when they should be using comments, and / or doing a lot of self-answering. I do think a cut-off or at least a reminder would be useful here, but if someone wants to slog through these and start flagging they could probably keep the moderators busy for a while... It's noise, but more than malicious it just seems kinda sad.
User % Below Threshold Total Answers
----------------------------- ----------------- -------------
Grumpy 29.787234042553 47
Sir Psycho 25.396825396825 63
Janie 21.739130434782 46
User % Below Threshold Total Answers
------------------------ ----------------- -------------
Arunabha Dutta Choudhury 66.666666666666 12
Joan Venge 50 14
unknown 46.666666666666 15
XcoderMi2 41.666666666666 12
-1 seems to be the more popular threshold, but frankly I don't think it's worth bothering. There are users with a lot of answers, and users with mostly negative-scoring answers, but the number of users with a significant amount of mostly-negative answers is tiny.