I don't like the idea. Class identity will be lost unless they make a lot of reprints. It would also make the game more expensive.
While I don't agree that the OP's suggestion would be good to implement I'd argue that class identity has already been lost & twisted for some classes.
For example, back when DKs were around Jaina turned mage from a class that intentionally lacked healing (in most cases) to one of the best self sustaining classes. Now, Khadgar Mage has turned what used to be a fairly spell heavy class into a more minion oriented one (which already happened with Elemental Mage in previous metas).
Shaman AoE used to be defined by overload drawbacks and still struggled with big minions (unless you used the rotated Volcano on tall boards with less than 15 health), but now can sit on board clears that reset the tempo for 5 mana.
Paladin had its aggro fast paced identity stripped with the removal of Divine Skill without having any other playstyle to replace the lost identity.
And who the hell knows what priest's identity is ever supposed to be (The vanilla IF priest? The old control, deathrattle, or N'Zoth type of greed priest? Midrange via Dragon or SS Priest like in old metas? Or OTK/combo like Razakus, Mecha'Thun, MB, or Gallery Priest?) Currently the class' unstable class identity in standard is combo (I guess?) via Nomi Priest.
I don't think resetting class identity would be that horrible at this point considering that it is inconsistently changed or preserved for almost all of the classes in standard anyway.
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How about play without base set at all ? Maybe it is not very good for free to play users, but set with 50 cards will more impactful, then we have now.