in combat healing in those games is extremely good... Close to prenerf healing spirit levels of good. Not only that, you mention phoenix down used in finalfantasy games. I may have missed the last couple, but those tend to be pretty rare and extremely rare
if you can get them. That style is how it worked in previous editions as described in my post earlier up thread
here & the included link it points to with the detailed breakdown
here.
Here are some quotes from those two posts...
1:"A big part of why combat in older versions felt more deadly was because recovering was either going to demolish your piggybank restocking that bag of recovery stuff you slowly filled through all these levels of adventuring or it's going to take so long you really need to go back to town " &
2:"In practice everyone would look at how much hp they were down & if it was really bad they'd probably go back to a town or somewhere safe so the casters with heal spells & abilities could safely dump all of their spell slots leaving them in an effectively helpless condition but if not too bad they might spend whatever heals they have left over & rest while eating the attrition or proceeding to use some consumable resources like potions/scrolls/wand charges". They moved away from the model you cite & that's part of the problem. With that said, in combat healing is pretty boring as a PC, you can do it sometimes... but it's not something particularly fun for anyone but the guy chewing through heals to keep being a badass.
A secret to turn-based RPG's is that healing, as an isolated action, sucks no matter how much it heals (even full health heals).
How good healing is depends less on the absolute numbers and more of the relative numbers. For example, a character that has 10hp that gets healed for 10hp has gotten 100% HP back. A character with 20HP that gets healed for 10 HP only gets 50% HP back.
What's more important, though, is the target's effective HP. It's basically having the defensive stats of the target put into effect. The real HP of, say, a mage and brawler might be the same, but the effective HP of the brawler might be higher due to his defenses. This matters because healing (usually) doesn't take defensive stats into consideration from the target. It's either a base number, determined by the caster's stats, or a percentage of HP from the target (which only accounts for the real HP).
To keep it brief, healing the brawler with the same spell is more effective than healing the mage or even the healer themselves.
Healing, by itself,
can be effective in D&D. From levels 1&2, a healer can recover an average of 7.5 HP which is close to maximum for certain 1st-level character and over half for most characters in-general. Your spell slots are low, though, and it's hard to manage them already.
In D&D 5e, being a dedicated healer that wants to keep people from going down almost requires you to go life cleric. Life cleric has many good things going for it. It turns cure wounds from 7.5 health to 11.5 which is plenty to top off all but the highest HP classes at 1st level. By 2nd level, they earn an extremely rare and coveted short-rest heal. Having a life cleric means that you can top off on health without spending HD or spell slots (this is extremely good).
Beacon of hope is good. Not in-combat while you might need concentration, but out-of-combat it can turn a simple second-level cure wounds to have 25 HP of healing, which is pretty great, actually. It also gives advantage to death saves, so if you're dedicated to being a healing type during combat, you have all the necessary tools. Most clerics perfer running around with spirit guardians, though. And I get the appeal of that. Personally, being a life cleric means I should focus on healing more (which I do enjoy doing).
Edit: AOE attacks just really are not that dangerous unless everyone is low. Tossing out a fireball might get a wince or two across the group, but5e is designed around the assumption that you start every fight with full health... tossing out the third or fourth fireball in a fight for the the 3rdfight in a row is going to give off some serious "killer GM" vibes & justifiably bring up "so I think gmbob is angry at us, is anyone thinking of starting a game or willing to gm?" between games the next time that happens in the session
Well, it's not about the AoE attacks in isolation. The point is to have multiple casualties at once so that the healer can't bring back multiple people up at once.
There's a couple of things to this.
1. Deadlier combat will always have a "killer GM" vibe no matter how well you think you'll hide it.
2. It's rare for a monster to have consecutive AoE's without them being limited. They're usually either on a recharge or a slot budget or a limited per day budget. The only monster I can think of is pit fiend and if you're fighting a pit fiend and fireball spam is
actually hurting your team, you've got bigger concerns.
What a DM should do is play the game as normal (mostly attack rolls) until the characters with heals and/or the character with low defenses are relatively low on health. Then, they bring out the AoE's. The exception is recharge enemies, who should actually have their AoE spammed as much as possible since it can't recharge unless it's used and their recharge is their strongest ability.