First of all check my name, I am a Taric main. That being said I played a lot of Swain before the MYMU and while his interactions are different, the stats he cares about and his overall role are unchanged.
Generally you want GLP for 2 reasons.
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It builds out of catalyst. If crap goes down and you can't afford to wait on a ROA then you buy this instead.
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Swain cares about damage to as many targets as possible. As such he prefers GLP as it slows a lot of targets instantly. His ult will only slow a few targets at a time with Rylais so GLP helps keep them locked down longer. GLP also has a 65% slow compared to Rylais 20%. That means he can keep everyone there, and Swain heals more the more targets there are due to how his ult targets.
Mana is also a super important stat so that right there puts it over Protobelt. The stats on it are also better. Protobelt also scales really badly. It is useful for it's utility, however Swain's W is delayed enough that jumping forward to cast it isn't going to be as effective as something like Annie dash into ult, so he doesn't get much from the mobility, especially since when running away he actually wants to stay close to keep healing, so dashing isn't effective that way.
Swain also scales for late so he doesn't want an item who's stats fall off as hard as Protobelt. It has some stats he likes, but the active isn't overly effective for him, the build path is sub par, the CDR isn't important on it, and although it is cheap and cost effective, that means that late game you are sitting on a weak item for a weak active with some OK stats that other items offer more of.
Basically like Morello. He can buy it, but doesn't actually need it, and doesn't offer anything to make it stand out over other items unless you are so far ahead you want it for more snowball power.
For stats:
Protobelt:
300 Hp (Good)
60 AP (Good)
10% CDR (OK)
Active:
Damage (OK)
Utility (OK)
Build Path:
OK, Kindlegem is meh, Revolver is Decent.
GLP:
300 Hp (Good) (Same)
80 AP (Good) (Better)
400 Mana (Good) (Better than 10% CDR)
Active:
Damge: (Good) (Better Base, Better Scaling, Hits more)
Utility: (Good) (AOE Slow > Short Dash)
Passive:
Good, but often unneeded if you have a ROA
Build Path: Good
Catalyst is very good, and often rushed. Can build this if you don't have time to stack a ROA
Revolver is Decent.