It's not more unfair, it's that the consequences of it being unfair are more concerning.
So the concern about the consequences is greater. Does this mean that when you roll for healing you are a bit more nervous than say, an attack roll, damage, initiative, or hit points for your new level? Like, is there a weight to the roll that makes you "insert superstition" to your dice because you have a greater want to roll high?
There's also a sense of feel-bad that I think is much greater with healing than with damage dealing. I don't know why but to me it always feels bad to roll low on HP when you heal or drink a potion or whatever... It feels much worse than when you roll low when dealing damage.
If something feels worse, there is no denying that it can influence from how a player sees classes, potions, spells, etc. It's a great point. I personally have never really felt that way rolling healing, but if it is because of the gated long rests or the consequences are more concerning, I can definitely see this as a great reason.
Can I ask one question: Does it also go both ways? If you feel worse rolling low for healing, then do you also swing high rolling well? (In my experience, damage and attack rolls are both high and low swingers. I am just curious if it is that way for you regarding healing.)
Damage output can slow down, but is unlimited, while healing is gated by long rests.
The gate thing is an interesting take when it comes to healing and far outreaches just this conversation. I mean, it could also be turned around and used as a narrative tool - something many seem to want from the game. Imagine a group traversing a dangerous area and needing to stop because they just can't continue. Their fighter is exhausted. Their wizard is hurt. Their cleric's communion to their god is weak. And their inventory is low. That scene could happen because of low healing rolls. It can be used to increase tension.
Of course, so much of the gated long rest is DM dependent, it matters little to the discussion.