I think GLP may need a rework possibly, or at least a buff.
Of the 3 hextech items, I believe that Hextech GLP-800 may have gotten the short end of the stick here. Protobelt's niche is that it helps the burst damage mages have their own little gap-closer as well as some CDR tacked onto it, and Gunblade is more for those Hybrid champs that utilize AD and AP at the same time and give them some more sustain to their attacks (I sort of view it as the AP Bloodthirster without the shield lol). As for GLP, it was meant for the Battlemage option since it builds with Catalyst for that sustain it gives, and gives it's own source of damage with the active that also slows. However, you never really see it that often on champions these days, mostly because instead, they're building GLP's main competitor, Rod of Ages. Why exactly, well because RoA is quite literally a stat stick that grows overtime to give better stats than GLP will.
Let's quickly compare the stats between Rod of Ages and Hextech GLP-800 shall we?
For the cost of 2700G, you get an item that starts out with: 300 Health 300 Mana 60 Ability Power
and over the course of 10 minutes, this item will get an increase of an extra 200 Health, 100 Mana, and 40 AP, which totals to:
500 Health 400 Mana 100 AP
At the same time, at the cost of 3000G, GLP gives you
300 Health 400 Mana 80 AP
As for the active, it sprays some icicles in a cone that deal 100 - 200 (+35% of your AP) to any enemies hit and slows them by 65% for half a second in which it decays afterward.
Whereas RoA has its stats build up over time, GLP gives them to you right away, at the cost that they won't be as good if you got RoA and waited until it was fully stacked. with the extra cost of 300g, in the long run you are losing 200 health and 20 AP. In fact, you could get a RoA AND a pair of boots instead of GLP and then get movespeed along with all those stats!
Now you may be asking, "Doesn't the active justify the extra 300G?" To answer your question, that one guy in the waaaaaaaaaaayyyyyy back over there that OBVIOUSLY asked this question: eeeeeeeehhhhhhhhhh?
The Active itself is kind of bleh tbh. The damage isn't too bad really, but it's main problems is that it was given the slow of an even crappier Karthus wall (I didn't even think that was possible lol), and the range isn't really anything to call home about either, but I'll forgive that considering this was meant for Battle mages anyway.
So here's what I'm proposing: Either lower the price of GLP to something that might actually be competitive (which I doubt will happen since this item DOES still give an active whereas RoA doesn't), or give it a better REASON to cost 3000G in the first place. In this case I'd say that the Active slow could use with a good buffing, and maybe increase the range to it a bit.