If this ever happens, I'd go for this 100%.

From what I remember, the Obsidian Amulet was given no teleports exactly because it would make it situational, instead of just being BIS and the best pick in every situation.
In that aspect it seems to have worked very well.

I'd be pretty hesitant with implementing amulet variations with unlimited teleports (let alone combining them). I guess it can be a hassle if you only have a single charged amulet, but if you charge at least a full inventory at a time, or multiple inventories (easily done with quest cape for dstone or simply walking from the fountain to the edge hub bank chest for slayer nowadays), it's not as much of an issue. It does take a few more batches if you aren't subbed on the character used to charged, I guess.
I personally just take two of each when doing clues or other kinds of activities that require a lot of teleportation. Alternatively I combine it with wearing a quest cape in case the amulet happens to run out of charges.

In many cases you only need one of each, and when using a slayer amulet to reach areas, it's easy enough to teleport out and back in for banking (just use quick-gear to refresh amulet charges).

I'd be very, very careful not to make anything like this too easy to get (I believe it's a 1 in 25.000 chance to get an eternal glory at the fountain of rune in OSRS?)
Do keep in mind that the wilderness is much more active/risky there, unlike this place where you can just find a quiet moment most times of the day). It's relatively easy to charge dstones once you've unlocked the requirements, but cutting away the charging entirely has quite an impact. 1% chance is still stupidly high in my opinion, for what it offers.

-1 to ultimate obsidian amulet from me personally
Not against dstone and slayer amulet variations with unlimited tps, but I'd rather see the idea more fleshed out first before slapping on a +1