And I recall seeing recommendations to charge them at much higher rates (eg, 40A).
I presume that in the linked Schumacher Battery Maintainer, "fully automatic" means it switches to 13.8V etc once fully charged.
It is done all the time - eg, vehicles, planes etc.
A vehicle's charging system is effectively a constant voltage charger - it tries to maintain a certain voltage (eg, 13.8V, 14.4V max etc).
However CHEAP chargers often output above 14.4V.
This is often true for trickle chargers (to quote.. "because they are only 1-2A, what damage can they do?". LOL! bang!)
Bigger chargers should have a 14.4V limit or cutoff but usually don't.
And once full, the charger should reduce to below 13.8V anyhow....
Batteries - so simple - a true Scientific Art.