I haven't seen any streamers who officially put their sub emotes on BTTV/FFZ/7TV and enable them in their channel, so if anything they end up supplementing the sub emotes rather than providing a reason to avoid subscribing.
Twitch could increase sub emote limits, but I'm not sure they would want to. Many emotes on FFZ et al are memes used in hundreds of channels and could not be used on Twitch even if copyright was not a concern due to violating many of the other sub emote guidelines:
So Twitch has no real reason to try and compete on this front. They just don't officially support it, which means anyone using the official Twitch app or not using any browser extensions will only see them as weird text in the chat. If Twitch updates the layout and breaks the extensions, the extensions will adapt, so power users get a ton of extra features at no cost to Twitch.
While these services make money riding Twitch's coattails, anyone willing to pay for the premium tiers of these services is likely either a streamer who wants to load up more meme emotes for their chat to use (increases engagement) or is the kind of power user who subscribes to multiple streamers at tier 2 or 3, so I doubt they hurt Twitch's bottom line. If anything, going to war with these extensions would likely hurt their bottom line since features like FFZ's audio compressor make many streamers' terrible audio settings listenable.
