The cleric is a very good healer so dont worry.
the problem is that 5E lacks a "Tank", you seem to think in MMO paradigms so ill put it that way for you.
Class roles in DnD dont work like they do in an MMORPG, several roles are not roles that come into play in combat, but rather come in play outside of it, such as the Party face or the much dreaded skill monkey (tho recet editions mostly did away with those)
That also means that combat is very different. For one, melee characters like fighters are primarily about dealing Damage (so think of the MMO DD) rather than battlefield controll ( like the MMO tank), with some side roles like a Paladin beeing able to heal.
The closest to tanking youll come in DnD is by bodyblocking people in a tight spot or by doing a Polearm and Sentinel fighter build.
In order for this to work properly theyll have to implement tunnel fighter tho which they probably wont.
As such, healing in DnD is not about having a fighter at full HP, healing is more utility than anyhting else.
A fight is neither won by damage spells nor by heal spells (at early levels, in the lategame, mass target damage spells like fireball and even more powerfull ones do end encounters quickly), rather the most important spells are crowd controll stuff like putting enemies to sleep or rooting them in place (if youve played icewind dale you probably know that drill from the bridge fight)
Anyway TL;DR yes theres gonna be strong healer options but no they wont do the same thing as theyll do in an MMORPG
