I agree that the rules in 5e prioritize dealing damage to healing during combat, but that's because:
1. Of the generous death save rules, there isn't a real need to get people healed during combat; and
2. Characters can "pop back up," and there isn't a strong need for full healing; and
3. Characters have a ton of hit points to begin with, and easily recharge between combats; and
4. The healing outside of combat is so generous, it doesn't matter if you're fully healed in combat; and
5. It generally makes a lot more sense to do damage than to heal, people will almost always prioritize doing damage than healing ... even if it's equal.*
*This is a math thing- in other words, if you take out X critter, then you avoid all damage from that critter. It's part of the "focus fire" strategy.
In-combat healing is a problem in search of a solution, because when the solutions are provided people don't take them. There isn't a massive demand for healing magic items - it's not like the staff of healing is the single coolest item in the game.
If this was a real issue, then the optional healing surge rules (again, DMG 266-67) would be much more popular. But they aren't. That said-
If you think in-combat healing is an issue in your game, then you should use the surge healing rules. Heck, use the optional optional rule to do it as a bonus action.