I was turned on to the Grace 707 tonearm in the mid 1970s.
I own a 707--it's taking up space in drawer somewhere. The bearings were the last thing I was concerned with. Smooth--no play.
However A) the horizontal (i.e., up and down) bearings are not angled to match headshell offset angle--not offsetting the pivot bearings will introduce an upward rotating arc on warps.
B) the headshell was made of a hard plastic which became brittle and eventually cracked. Fatigue from old age. I Superglued the peices back together and other than being ugly that worked.
Changing carts on this device was not an easy task. It required at least three hands and fifteen fingers. Years later, with fumble fingers I broke the anti-skating wire. LOL
How concerned should I be about “play” in a gimbaled tonearm bearing and how much effort should be exerted into making it free of play?
From a practical engineering standpoint, there is really no excuse for loose bearings. That problem was solved years ago.
The only tonearm I recall owning that had loose bearings was the Thorens TP-16 arm that came with my TD-160. The arm was generally ergonomic and sophisticated--magnetic anti-skating, dynamically balanced, straight tube with plug-in headshell making cartridge changes easy. But you could move the arm tube back and forth inside its gimbals. However, that was the least of my worries because I could never get the suspension to work well in my room.
I have a Dual 704 (1977, contemporary with the Grace 707) and the arm still works as new. Smooth bearings with no play.
My Garrard Z-100 pantograph arm has 6 bearings (to control up-down and sideways movement along with the rotating variable headshell tracking angle); no play in any of its bearings. I'm amazed at that--the engineering that went into it at the price-point.
My Technics SL-1100a and 1200 Mk5 have no bearing play.
@Robin L has it right. The beauty of records is that they give you something to worry about. You 'correct' one thing and you still have a dozen other things to obsess over. It's the perfect format for the neurotically inclined. I guess that means me!