However to go on to say that no Pokemon should have access to coverage moves that allow a prepared trainer to take out what would be counters

Not "counters" Pokemon that are HARD counters for your type, as in you're not actually supposed to be just beating an equal level Pokemon because you have a move they're extremely weak to

Garchomp (a dragon/ground type) can get a move like Iron Head (a steel type) which, with Garchomp's already impressive spread and attack stat provides it a solid hard counter to both Ice and Fairy type Pokemon, who should otherwise wall Garchomp out of the fight.

Fairy and ice aren't supposed to hard counter ground or dragon

You're confusing checks and counters, a counter is supposed to be an inherently you switch or die choice, a check is supposed to be something you can get by via coverage moves and generally being prepared

Garchomp is checked by fairy and ice, but it's not a hard counter, and if that garchomp gets unlucky or isn't properly trained, or even gets outsped? It can very easily die without OHKOing it's checks

Moreover, one (well a handful of) Pokemon being broken isn't a reason to keep the ability to counter hard counters on most Pokemon Esp when those Pokemon have been relegated and banned from alot of competitive tiers specifically because of it's power