HP regen itemization needs improvement.
HP Regen really should be a valid tool for champions who are weak in the early game to survive lane.
If they want to just hang back and survive, it can help them do so without giving them some absurd capabilities in combat.
At the moment... it just kind of sucks all around.
In League, HP regen is measured in HP5. I don't like this, since it just artificially inflates your perception of how much regen you're getting. As such, I'll be using health/second.
The way HP regen works is that your champion has a base amount of regen based on their level, and any HP regen items add more regen proportional to your base regen.
The highest HP regen value at level 1 is on Sion, (though it used to be Heimerdinger, rip that build) with 2.036 h/s. The lowest at level 1 is Soraka, with 0.5 h/s In the past, you could augment these with regen runes/masteries if you wished, but there isn't currently a proper regen rune in any tree (except Revitalize, and even then only 10% and when you're below 40% hp).
7 champions are below 1 h/s at level 1. 80 are between 1 and 1.5 h/s at level 1. 51 are between 1.5 and 2 at level 1. 1 champion is above 2 at level 1 (our boy Sion).
Seeing as most are in the 1-1.5 range, lets use 1.3 as a ballpark average for how much regen the items are gonna give you(I'm not gonna punch in 139 values).
The items that give % base HP regen are as follows.

Items that give regen calculated other ways are as follows.
4 h/s
3-5 h/s
0-5% max HP in h/s
multiplies the end value by 1.3
Now, how much are these actually giving you?
Going back to our ballpark average of 1.3 h/s, we can calculate that. I realize that these are level 1 values, so they'll be a little low, but HP regen is important when it comes to sustain in the lane phase, so it's in the right neighborhood.
will regen 0.65 h/s.
will regen 1.3 h/s
will regen 1.625 h/s
will regen 1.95 h/s.
will regen 2.275 h/s.
will regen 2.6 h/s.
Out of those,
are generally only bought on supports.
are just component items.
don't get bought often in general.
normally only get bought in top lane.
are only bought on tanks.
is bought at a point at which hp regen is pretty pointless.
is only bought on tanks and its passive makes other regen itemization pointless.
If you're a top laner who doesn't really want any of these specific items, you don't have a regen item. If you're a jungler who isn't a tank, you don't have a regen item. If you're mid laner or ADC, you don't have a regen item. If you're a mage support, you don't have a regen item.
It just kind of feels like HP regen is thrown onto tank and support items as filler text to make the item seem like a bigger purchase, but it's not, really.
You aren't buying any of these items because you need health regen. Nobody cares about it, but looking around at other games, it can be a really nice stat to have lying around.