Q:

Is changing concentration rules for 1h+ buff spells a bad idea?

I have noticed that many long duration (1h+) spells in 5E D&D have concentration, effectively meaning caster cannot cast other concentration spells while using such a spell (or end the spell). For example Barkskin and Alter Self. This seems to make many "buff" spells much less useful, possibly to the point they will never be used except very in special circumstances.
I have played and DMed since early red-box basic, and I get that 5E with its bounded accuracy is not like 3.5E where the Wizard would buff up party with 4-5 spells before they go to work for the day. However it still seems weird that now you would almost never do that or any concentration buffs in 5E. I get that with reaction spells you may not need buffs as much - but I liked the strategy and planning of selecting buffs.
I am thinking of a house-rule something like this:
Besides Concentration, there is Subconscious Concentration, which works the same (only one subconscious spell at a time, which can be lost if concentration would) - but it would allow you to have 1 Concentration and 1 Subconscious Concentration spell at the same time.
Generally longer lasting (1h+? 10 min?) non-damaging utility spells would be Subconscious Concentration instead of Concentration*. This way the Druid could use Barkskin and still cast concentration combat spells and have fun in a fight.
However, you would not have a stack of expected standard buffs on the party either, since only one utility spell could be subconsciously concentrated on at a time, which I think would make for interesting choices.
*Obviously I would have to evaluate spells for subconscious mechanic individually.
I admit I am on the fence re Magic Weapon since it is damage causing - but I like idea of wizard buffing fighter with a magic weapon as they hunt that Werewolf, while still being able to cast a spell or two during the fight. On the other hand I think scrying would probably stay regular concentration because...it feels right. 
Is this a good / bad / unbalancing idea?
What are some Pros and Cons?
Any suggestions for improvement on this house-rule?
Edit: Conclusion
Thanks to everyone for feedback and sharing your opinions. It seems this house rule might be a bad idea with unbalancing consequences.
1) DMG p263 strongly advices against changing this part of system. There will probably be balancing issues, not limited to casters outshining non casters. Haste or fly + long term subconscious buff does give me pause.
2a) wizard still has many non concentration spells like fireball
2b) druid is more limited in options but with wildshape combinations this could be a design feature rather than a bug. Call lightning with a flying creature comes to mind. If the barkskin concentration limit that got me thinking about this in first place bugs me it may be safer to just make barkskin non concentration rather than risk braking everything.
I am having second thoughts about the wisdom of this house rule. If I do give it or something like it a try, I'll update on how it turns out.

A:

The game was designed with concentration in mind. If you change how concentration works, it will almost certainly be unbalanced, unless you take steps to actually balance it. 
That being said, it's your game. Try it, see if you like it. If you don't, then change it. When I am thinking about changing something, I usually search for the most broken scenario I can think of and then I play test it myself. You would need to list everything single spell viable for this new mechanic and then try stacking different spells together and see what happens.

A:

You know many Wizard damage spells are instant and can be cast while concentrating on something else, right?  e.g. Fireball.  You're intended to be able to Haste a party member (or other buff spell) and then blast away.
Having Haste plus a "subconscious" longer-term buff up simultaneously and still being able to Fireball seems pretty powerful.
I think the main competition for a Wizard's concentration slot isn't damage spells, but rather short-term very strong buffs like Haste.

It's more a problem for Druids where most of the damage spells are concentration (Call Lightning, Flaming Sphere), although most of their damage cantrips are still instant.
I don't have a lot of experience with this, but yes I think Barkskin is hard to use because of the concentration opportunity cost.  Perhaps if you're worried about an ambush?
But druids can do a lot of stuff (like wild shape) so I think the existing balance (of many druid spells requiring concentration) is fully intentional.  e.g. Call Lightning then wild shape into a bird to stay out of reach while blasting enemies makes it an upside, and saves your spell slots for later healing.  It does mean you can't buff.  Or the classic is Flaming Sphere + Wildshape so you can attack and move the sphere with a bonus action.
Or if you wildshape into something squishy, barkskin first.

