Tony Vargas
Legend
What you're getting at is that there's some dedicating healing resources (HD) in 5e, and some multi-purpose resource (slots) that can be used for healing, or other things. In the classic game, healing came from spells and from found items. In 3e, from spells and from cheap made/bought items. In 4e, almost entirely from Surges, with foundational surge-triggers also dedicated, healing powers could only be 'converted' when re-trained at level-up. When you have a ready resource for dedicated healing, be it HD or WoCLW or Surges or what ever, /and/ you have a multi-purpose resource that can be used for healing or for many other things, the tendency is to avoid using the multi-purpose resource for healing. The more flexible the resource that can be used for healing, the more likely it'll be used for something else. In 3e that contributed to CoDzilla. In 4e, class & encounter balance. In contrast, in the classic game, Healing tended crowd out daily spell loads for casters that had it on their list, making the Cleric the un-popular 'heal bot.'5e healing is a lot less "liquid" than any previous edition other than 4th. Editions 1 through 3.5 relied on healing through magic from specific sources, whereas 5e has a significant amount of healing on a per-character basis from HD. Compare to the editions where rest healing was a few points per day, where healing resources were actually pooled together.
5e, in keeping with it's goals, take a middle-of-the-road approach. There's dedicated healing, but it's limited in both availability (its the slowest-recharging resource in the game) and quantity (1/3 to 1/5th what it was in 4e, relative to PC hps, though PC have a lot more hps at high level, and a lot less at very low level). There's spell-slot healing, but it's extremely flexible, being chosen round-by-round, and low-overhead (you only need to prep one healing spell to be able to use a slot of any level to heal in an emergency).
Depends on the DM and the enemies. If enemies are using basic tactics like focus fire and prioritizing targets, lack of sticky 'defender' mechanics results in damage being concentrated on one high-value target, like a vulnerable-looking caster, first. If enemies are heedless warriors trying to prove themselves against a 'worthy' foe in single combat, or otherwise looking for individual victory, sure, it'll get spread around.Furthermore, in 5e compared to 4th ed (and 3rd ed in some cases), defensive-capable classes are much less "sticky". This leads to damage being spread around the party a lot more, rather than the Defender-type classes being able to focus much of the incoming damage upon themselves.