I find that 5e priests tent to play the same from game to game, so something that encourages more differentiation would be welcome. That said, I would be wary of ending up with something like: "3 of these 5 'best' domains are the only ones picked, so now clerics have a narrower list in actual play so there's even less variation. Oh, and only have the deity list gives access to them so there's less variation in who you worship as well - your RP choice of another god can hamstring you mechanically".
An issue is that there really are some stand-out cleric spells so you see them over and over. If there were more spells of that very high caliber we'd see more variation, even without enforcement. But I haven't seen a cleric without most of spirit guardians, spiritual weapon, guidance, bless, and a few other staples basically ever in 5e.