Wrong, wrong, and wrong.
Karma does not roam. Janna does not roam. Alistar likes to stay with his ADC. Support Vel'Koz likes to sit with his AD and protect them from ganks, keeping up harass as well. Zilean can't roam well at all without giving up experience needed for levels in Chronoshift.
The 'high level support streamers' you watch are sacrificing GPM for health lategame, due to FotM's shield passive synergizing well with Thresh's lantern and with Mikael's. You know why they 'basically give up on ever trying to get Relic procs'? Because there are hooks, there are stuns, Alistar combos, and Blitz grabs to be landing.
'Unless they .. have nothing better to do.'
You know why they don't bother with Relics and why it doesn't take priority? Flay autos are used for harass and extra damage on carries that are hooked. Using these flay autos on minions creates spots of stationary Thresh, sacrificing harass or aggressive positioning for higher GPM.
If you depend on high-level or high-MMR streamers for all of your game information and build paths, you really, really need to spend more time on the game yourself.
Pros aren't always doing what is the best.
High-rank aren't always doing what is the best.
Someone taking Relic on Thresh, knowing full well that you're taking the selfish stat (health) over mana regen and a free disengage/engage active (Talisman) late game, without being able to proc the heal reliably, is no reason to have a ranged champion (Thresh) be able to proc the passive without some type of sacrifice.