It boils down to this: the warlock only does a few things, but does them ad infinitum. If the warlock picks invocations that turn out to be weak, then he'll always be doing something weak. If he picks something that's easy to exploit, then he'll be exploiting the heck out of it. "All things in moderation" is one of the better homilies out there for a reason, folks.
Sure, it's pretty handy for the party to have a warlock that walks around using dark speech to shatter everything--and I do mean everything--but it's also a pain in the neck for the guy running the campaign. Likewise, it's annoying to have a class that makes invisibile creatures pointless, or who you can count on to fill up every battlefield with masses of chilling tentacles, or who tries to charm every NPC and monster encountered. Now, please, nobody try to regale me with all the various ways these specific abilities I mentioned can be mitigated; not only are you unlikely to think of anything I haven't thought of, but you'd be kind of missing the point. Invocations will be in non-stop use, so any countermeasures have to be nigh-constant as well.
Worst of all, the player in question has every reason to think he should be allowed to use his invocations at every opportunity. It's what the class does (and the character being evil or chaotic doesn't help in the self-policing department either).
Looks good, plays bad.