Several people have already suggested adding a new category of emote slots for viewers who gift subscriptions or for viewers who have long subscription totals or streaks.
Instead, I propose reworking (and likely renaming) Bit Emotes to allow viewers to progress toward them with the value from gift subs, self-subs, and donations through the charity tool.

With the current iteration of Bit Emotes, most channels will never unlock the majority of the slots, because the thresholds are scaled with the platform's largest channels in mind. It's not unheard of for a smaller channel to unlock a lot of slots because of one or two viewers who have the means to give a ton of bits, but then almost nobody has access to the emotes assigned to those slots. Simply adding a new category of emotes would repeat the same problem (the thresholds would be established based on the largest channels, most supporters would never unlock beyond 1 or 2 of the emotes, and most of the potential slots would never get unlocked).

Opening up Bit Emote thresholds to include other types of support would help existing emotes gain better circulation, help streamers access more of the locked slots that already exist, and provide a reward/incentive for users who enjoy supporting through Twitch-specific methods other than Bits.

Counting the purchase of a subscription (regardless of whether it's a self-sub or a gift) would be a great way to add more value (gift sub recipients would not gain credit in this way, just the purchaser). This would also have a baked-in incentive to consider Tier 2 or Tier 3 subscriptions, which currently don't carry much incentive.

Obviously, a significant obstacle in including sub value is the disparity in subscription prices in different regions (whereas Bits thresholds are uniform regardless of how much the viewer paid for them), as well as with streamers who have negotiated custom sub splits. I believe it's possible to arrive at some kind of standardized point model, whether it assumes an estimate per support method (eg "each Bit or purchased T1/T2/T3 has a set point value regardless of purchase price") or a calculated value (eg "each support method provides points directly calculated by the payout value to the streamer" which might get complicated if the streamer relocates to a different region).

To clarify a little bit: imagine the purchaser of a T1 sub gets (for example) "250 bits worth" of progress toward permanent emotes. It would take 20 months of T1 subscribing (or 20 T1 gifts) just to reach the second Bit emote. This would not make Bits obsolete, but it would allow greater material reward than sub/gift badges that are only visible in the channel itself.

Prime subscriptions could also be factored in, as they still provide measurable support.

Twitch's built-in charity feature is relatively new as of this writing, but it's easy to imagine similarly allowing charity donations (made specifically through the charity tool) to provide equivalent progress. I could see people disagreeing on whether or not charity donations should be factored in, as they don't directly support the channel itself, but I feel like most streamers who feel strongly enough to run a charity event using the tool would be comfortable providing a built-in incentive (and failing that, there could be a setting to allow the streamer to decide).