The problem with this feat is how to apply it to a d4?
With 16 con, your minimum is 6 on a d4.
What has higher precedence?
The maximum of the die or the newly set minimum.
There are no classes with a d4 hit die, so as phrased, the question is moot.
However, if you had a Cleric, Wizard, etc. with 20 Con, then you could have a situation where 2x[Con Mod] is greater than the hit die.
Personally? I think the feat should give you that minimum value. So you (effectively) don't bother rolling--your hit die healing is beefier than anyone else's. You've invested an absolute metric crapton into your Constitution, and taken an otherwise pretty much garbage-tier feat. I say, reward that choice with making a character
genuinely stupidly durable.
Even a Barbarian could face such a question if they hit level 20, since in 5.0 your Constitution can be increased to a maximum of 24 and thus your modifier becomes +7, despite your hit die being d12. But, again, if you've invested
that hard into being just Stupidly High HP, and you single-classed Barbarian for
twenty levels, yeah I kinda think you've earned your ultra-fat HP.
It's only going to give characters something like +40 HP over the course of a day. Is +40 HP, when the character has something like 4x20 + 6 + 4x19 = 162 HP, really that much of a big deal? Yes, it's a perk.
Is it REALLY such a powerful, unsound perk that we should block it?
I say, let it ride. Someone going that much all-in for survivability, particularly with such a weak and roundabout way of doing it? Sure, knock yourself out. Or, I guess, avoid getting yourself knocked out? I don't see the point in slamming down hard on something that is incredibly weak in charop terms.