This is actually rather more efficient than "regenerate target creature" usually gets. Most repeatable sources of arbitrary regeneration are card disadvantage (Tel-Jilad Lifebreather, Fanatical Devotion, Medicine Bag, Draconian Cylix, Savage Thallid etc). (Well, okay, not card disadvantage because you're saving a creature, but card-advantage-neutral. (Card neutravanatage. Nonplusorminusvantage. Evenvantage. Uh, is there a word for that?))

The ones that aren't card neutravantage are powerful rares (Yavimaya Hollow, Asceticism), rather conditional (Vagrant Plowbeasts, Sporeback Troll, Jhoira's Toolbox), require quite fiddly mana (Ragnar, Niall Silvain, Suture Spirit, Orcish Healer) or otherwise fiddly circumstances (Molting Skin/Broken Fall, Horizon Seed.

So while gaining 3 life a turn for an investment of 4 mana or is fine, I think regenerating arbitrary creatures for just 2 mana or just might be a bit stronger than you intended.

Yeah that is a little stronger than I had intended. Though I noticed that most of your cards for regeneration comparison from modern magic didn't require you to tap to activate it. I'm gonna up the activation cost to match the other ability.