And I'm saying you don't need more than your existing number of hit dice, maybe coupled with the Healer or Inspired Leader feats, to play 5E within reasonable bounds.
That is, you don't need cure wounds spells or some such just achieve the default balance.
Ergo, you don't particularly need more Hit Dice just to keep the game from falling outside expected bounds. You certainly can add more Hit Dice, but it's not something you need to do or the game becomes atypical.
See it as a change on par with allowing or disallowing feats. You *can* make the monsters harder to compensate for the addition of feats, but you don't *need* to. Maybe you *should*, but not reflexively, and only if you think your players would be bored otherwise.
For standard 5e, I agree with you. But we're discussing a house rule where healing requires you to spend HD to have an effect. If you want to maintain the same level of difficulty, then you need to do something (with the most straight forward approach being to boost HD so that it keeps up with expected magical healing).
Put another way, a typical 1st level character has 1 HD. But, if there's a healer, they also have that healing to fall back on. And maybe a healing potion or two. That can easily be an additional 2 to 3 times max HP. As such, if you require them to spend a HD to benefit from magical healing, you've undercut their reserve HP significantly.
Sure, players can work around it with feats, but there's no guarantee that feats are allowed. Even if they are, is the DM going to mandate that players take these feats?
Don't get me wrong, I liked the idea in 4e and I still like it. It reminds me of the healing from the Wheel of Time, where magic could greatly accelerate healing but drew on the target's own stamina to do so. Too much healing could literally kill a person, and it explained why some injuries couldn't be healed even with magic.
5e is also a very flexible system that can tolerate a significant degree of modification without breaking. That said, a DM should always consider the potential consequences of any change that they make, including whether that change may necessitate additional changes.