I think Tanistry should've been available to Celts from the start, it should be available to both tribal and feudal characters, and Irish rulers should probably even start with it in place of Gavelkind.
I haven´t played with tanistry (or indeed, any irish character) yet. Why is Tanistry better than elective etc., what is so special about it?
Tanistry is essentially a better Seniority (instead of the oldest dynasty member you get a distant cousin with decent Diplomacy), but whether it's better than Elective Monarchy depends on how well you can control the vote and whether or not you're running an eugenics program and on what attribute you're focusing.
For example in my last game I set up myself with a size 12 Demesne and made sure my heirs were all Midas Touched Geniuses with enough Stewardship to maintain said demesne. Tanistry would've wrecked havoc on that particular setup. (The succession I was running was Elective Monarchy with myself as the only voter.)
Likewise if you set yourself up with a 6 castle capital and high Martial Education to get the maximum personal levy, you would again get screwed over by Tanistry when you get an elected heir with low Martial skill.
However, if you have a demesne of 7 or less (depending on centralization laws), are not running any sort of eugenics program, and use vassal levies or mercs or retinues for most of your fighting, then Tanistry is probably the best succession law available.