First off, RE: the part in bold, it looks like I typo'ed. When I first started playing, I expected HD healing to be sufficient and
magical healing to be unimportant, because of how weak clerical healing is. What I didn't realize is that clerical healing is not even close to a ceiling on effectiveness.
As for the gishy superhealer, have a look at my post here as MaxWilson for details: (
http://www.giantitp.com/forums/showthread.php?471899-Ridiculously-good-healer-(just-for-fun)). The gist of it is stacking Aura of Vitality (70 HP healing) with Extended Spell metamagic for one sorcery point (140 HP of healing), and also with Disciple of Life (240 HP of healing).
Even if you roll poorly on stats and can't afford a Str over 10, by level 10, you'll wind up with a plate armor-wearing, Con save-proficient superhealer with good melee and range capabilities. Mobile cancels out the movement speed penalty from plate armor (Longstrider would too of course, but I like not having to spend the spell slot, and having Longstrider in reserve) and also enables Booming Blade tricks. With only Str 10 her to-hit isn't anything fantastic, so she's not as good as a real gish, but still not bad. That's half of what I meant by "surprisingly gishy", and the other half is the way she can cast Blur and Shield to tank if she wants to, or just drop a Careful Web on the party (to which PCs will be immune because careful) which makes it basically infeasible for melee enemies to engage you while you're standing within it. By level 12 she can be a warlock 2 with Agonizing Repelling Blast, which makes her even better at range and at support tasks such as blasting enemies off cliffs and into walls of fire. Access to Bless is just gravy, and having four or five uses per short rest of Cutting Words is a lot like a Shield spell that can go to anyone in the party--or you can save it for skill checks and saving throws of course.
Does that answer your questions about "why not life cleric"? Bards are already better healers than life clerics thanks to Aura of Vitality, even before you consider Extended Spell shenanigans. Also I hate playing clerics, which is probably the single biggest reason why this build has remained theorycraft for me and not something I've actually played. (Well, that and the reason that I mostly DM.) But because I'm a powergamer at heart, my RP objections to clerics are warring with my powergamer instincts, looking for a compromise that can satisfy both...
Final comment: a superhealer will have Stealth and Perception expertise and is not unlikely to have a Stealth skill of +10 or better relatively soon, but unlike a Rogue she doesn't have Cunning Action to exploit it during combat. Don't let that stop you though. Sometimes, Hiding with your regular action is a perfectly good choice especially if it lets you e.g. stay safe/untargetable within darkness while healing someone every round with your bonus action (Aura of Vitality for 2d6+5 thanks to Disciple of Life, for twenty rounds in a row thanks to Extended Spell). Don't feel like you absolutely have to do damage every round.