Generally, tinkering with activation mechanic is less safe than one might think, especially if it jumps the random/nonrandom border or overloads some unit stat. In any case I wouldn't really go with a trivial alternating activation scheme in any game as I've found it too prone to activation rushing, but of course that's just our group (we spend some years developing and testing a non-random system to alleviate the problem and it's still open to debate...).

Technically, I suppose there isn't much it'll directly affect tho, except for making Commanders rather overtly expensive. The rest of the effects such as individually fielded models gaining usefulness beyond their points are results of the activation system artefacts.

While I don't agree random activation removes strategy (tho it introduces "fog of war" and does remove some of the "all-seeing eye and all-knowing mind" advantage of the player over a real-life commander), this is of course very much "to itch his own" kinda thing.

I personally find activation rushing such a serious artefact that I accept random activation (or more specifically "stackable random activation" as in the case of Defiance) as an acceptable solution for removing it. I like to think our method of nonrandom balacing is slightly better (no surprise there), but it's not trivially exchangeable...

If you find the activation rushing a negligible problem at best (some people for example argue that small units are so fragile they aren't a viable solution for pumping up your activation count, thus making it a moot point) there's no reason for not to change it for your private games of course. Just be aware that changes -- possibly surprisingly radical -- in the dynamic of the game are to be expected when you do.