The only legit reason I can think of for allowing unlimited edits is pride. eg.
My reply has “teh”, “theyre” and I change to “the”, “they’re” to conceal my lack of typing skill.
(I usually catch these during the grace period)
I answer
- ABC
- DEF
- GHI
log out, get some sleep, wake and while eating breakfast realize “OMG!! I forgot to mention JKL !!”
Personally I have no problem posting a follow up reply saying “D’oh! I forgot to mention JKL 
” but I can understand that others may have appearances to keep up.
Discourse already has a Wiki feature for posts that are likely to need frequent updating.
And I would rather get a Notification for a topic that got a correction / additional information post than get a Notification for an aged post that got edited.
IMHO if a topic is old and no longer relevant it should probably get some type of “deprecated” post pointing to the up-to-date topic.
But,if that doesn’t work for your forum, as Jeff said