Sorry but I will need you to take your crusade elsewhere.
I thank you for your proposed solution #3, which actually addresses my problem, but otherwise I am not interested. You see, my players are already not interested in the healing role, and so perhaps we can agree that you are not helping in any way: I definitely will not tell my players they're playing the game wrong, or that there is anything wrong with what they like or dislike about the game.
What I need you to understand is that I am asking for optional rules. As in "rules not in the Player's Handbook". As in "rules you can freely disregard". As in "rules you are not entitled to stop discussion about". Thank you.
I'm sorry you feel that way. But what I tell you is that people need relatively little to feel entitled to something, and as such any good solution that comes from any place remotely official looking can be grounds for it. Take for example Feats and multiclassing, officially they are optional, but I know of many people who will refuse to play with any DM who doesn't want them. The same with a killer rule that makes healers unnecessary, as much optional as you want to make it, players will feel entitled to it eventually, and that will be very hard to disregard the day a healbot player lands on your table. The danger from it coming form an official source is that this will repeat on many tables to the point that eventually no healer players will feel welcome on any table. (If you still aren't convinced on how easily people feel entitled, just notice how you just told me to talk only about what you want when you are not a Mod nor the OP of this thread)
It isn't your players are playing wrong, but their attitude towards the healer role could certainly improve. As such came my suggestion 1, bring in an additional player who would love to keep your players healed, I'm not telling you to ditch your players and replace them, just to supplement them. If not, my second suggestion, if you want them to share healing duty, make a healbot NPC and have them share it with they taking turns to play it, just don't replace this NPC right away if it dies, this has the added benefit of they eventually caring about it, and if a healer player ever lands on your table, well the rest of your players will be grateful as he/she will be taking away an external source of power, not something part of of their characters.
This is also the thing, why are you worried about this issue? have your players complained official adventures are too hard? Have you TPK'd your party? Is it only you who cares? Are your players worried they don't have enough healing? I don't know about the context that makes you care.
HD and an insane amount of potions should already do the trick, if you feel they don't, just make the potions stronger and turn hit dice into healing surges (equal in value to 1/4 total hp, and with a number equal to average Hp/lv per class), or make them fully refresh in a short rest. You could also allow the medicine skill to be used as an action -or bonus action if your party is specially picky- to allow someone else to spend healing dice (Dc 13-15 or something like that). Or rule that all Hit dice are maximum.
it would be nice if the party could do without a healer, but when one is present, everybody notices the welcome heal-bonus!
But well, the threshold between useful and required is thin, as is the one between not required and useless. One player "hey look I'm awesome at healing" can easily be another's "I have to play a healer, having one is so good we need one no matter what", conversely one table's "we can go on without a healer" easily turns into "we don't want a healer, they don't pull their weight" in a different one. Or one player "Well I'm having a moderate effect on the party" is easily "I'm having no effect on the party" for another.
You're misreading the counterfactual. It's not "Would the PCs be less successful if I was playing a different character?", to which the answer, in an even remotely balanced game, must be "not really". It's "Would the PCs be less successful if my PC was not there?" And that's as true for a healer as for a fighter or MU.
Probably this is the problem in here, my worries are more centered on the answer to the question "Would the PCs be more successful if I wasn't playing the healer?", or closer to my fears "Am I harming the party by playing the healer?" the less beneficial the healer is, the closer to that question being "Yes, you are harming the party, you are causing them to get hurt, having longer combats and are wasting everybody's reduced game time".
Of course a party with a healer can accomplish more than if it lacked the healer. The issue is, should it be able to accomplish more than if it substituted a skirmisher, or a wizard, for the healer? I'm happy if the game gives a marginal reward for the synergy of diverse PCs - D&D is a party-oriented game, after all. But I don't think those benefits should eclipse other options. Choosing to play the second warrior, or the second archer, rather than a healer, should marginally increase the skill needed for the party to act at full efficiency. It shouldn't be crippling.
Of course I don't want the party to be crippled too much when playing without a healer, but the more you make sure the party isn't crippled without a healer the more you cripple the healer by necessity.