What is stopping you from being part Lich, part Death Knight, and part Ooze Lord all at once? The chains being psuedo-class identities is strange. Ah yes, I am a Death Knight Gish, but my main class is Barbarian
I guess the concern is it goes against previous lore somewhat.
The canonical way (at least as far as I know) to become a lich is to embark on a convoluted fetch quest to bring together some 10 or 12 exotic ingredients, which you use to craft a philactery and perform some sort of ritual suicide with. Then you emerge as a lich.
While you have all but one of the ingredients, you may be very close to becoming a lich and yet also 0% a lich. And you may be at that rung on the ladder for a limited amount of time because some of the ingredients had a freshness requirement and if they grew stale you would need to find them again, but anyway that’s besides the point. The point is, you could amass most or even all of the ingredients and then not follow through with it, and walk away, but in the original lore if you did that you would be 0% a lich, not partway.
Once you did become a lich, there was (again, if I remember correctly) one more epic level progression beyond that which was to turn into a demi-lich, which was just the skull floating around. So that was a bit of a path, though that is not captured in the UA content.
With this UA feat path, you are kind of taking baby steps, in particular having a philactery which doesn’t do much for you and might even be more of a downside overall. For purists this may be straight up wrong. For more open minded folks it may just be yet another iteration of lore, to be thrown in the heap of past lores and just as valid, even if different.
As far as I’m concerned, I’m not a fan of either of the two paths (DK and lich) in and of themselves, but as I tried to make the case, I’m a fan of the "prestige feat path" mechanic in general.