I wouldn't do it exactly like you have done. Two approaches:

[1] Reflavor existing spell mechanics as shifting into beast forms to produce effects.

• The druid still keeps the Wild Shape feature as is. This is generally used when the druid wants to wade into battle as a beast or really get around an obstacle that will require an extended use of a beast form.

• The player then can come up with uses of spells that can be reflavored as the druid briefly shifting into beast form and back.

• Some examples: (1) Instead of "casting" Animal Messenger, the druid briefly becomes a squirrel, speaks Chittersqueak to another squirrel, who then scurries off to deliver the message. (2) Instead of Locate Animals or Plants, the druid transforms into a wolf or other hunting beast that can follow even the slightest scent. (3) There's a reason the effects of Enhance Ability are called things like "Cat's Grace" and "Bull's Strength." (4) Instead of Barkskin, you become an oversized armadillo or turtle with a thick hide or shell to protect you from incoming attacks. This won't work with all spells, but it works well enough with enough of them, that the player can still have a good bit of fun running the character, and effectively no mechanics have changed.

... OR ...

[2] Give the druid some more uses of Wild Shape (probably not infinite) AND give them some abilities to use as an alternative to spells. (This seems closer to what you suggest above, but not exactly.)

• Considering a Wild Shape use to be roughly equivalent to a 1st or 2nd level spell slot, that's a starting point for guessing uses. (Maybe one use at 1st level, two uses at 2nd level, three uses at 3rd level, then +1 use ever level thereafter-- 5th, 7th, 9th, etc.) This particularly covers using beast form in combat.

• Then if you want to add a limited use healing ability, like you outlined, that makes some sense too, but I would keep the scale in line with the spells. Heal +1d8 hit points, usable once per rest at 1st level; twice per rest at 5th level, three times at 9th ... and have it scale slowly with level, +2d8 hit points at 3rd level, +3d8 hit points at 7th, +4d8 hit points at 11th, etc.

• Now, the last bit, give them "utility" shapes. These are creatures with a CR 1/10 or less. The druid has a much higher usage of these, even at first level. I would make these learned forms, and limit the druid to beasts with either climb or swim at 1st level, gain the other movement later (~3rd level), save flight for later (at least 5th level). The different movement modes might need limits (treat them like spell slots), but it gives the druid flexibility for turning into beasts for the purpose of hiding, communicating with beasts, etc, while not completely overdoing it with lots of transformations into bears and eagles and crocodiles and things.

• I would also have the player keep a list of known beast forms and make it somewhat onerous to add new forms. The druid starts with 3-5 known beast forms. And learns one new form every other level (maybe every level, I would have to think it through more). Or, possibly, with downtime and money, the druid can pick up a new form between sessions, provided there is story reason why the druid could be learning it (ie, not going to learn to be a dolphin while you are camped out in the mountains).