"Anonymous. How would you know where beat three is if you don't count."
By feeling it.
"Without counting it could be beat one."
No, beat one feels different.
You really have no experience with music, do you? If you listen to a great jazz soloist, do you think they are counting the beats and remembering the changes, and knowing that because this is the 3rd beat of the 5th bar they should play in a certain key? No, they listen, and the music speaks directly to them. They participate in the music directly, without having to go through the extra stage of numbers and conceptual names.
As will a DANCER, only their body is their instrument.
But music students, like dance students often need to count as they first learn to figure things out.
"Your paragraph three. strength to keep in time. Try doing the Reverse Turn correctly and your two quicks will be balanced. Do it with a left side lead you will be off balance."
That's not where is strength is needed. The primary problem with foxtrot timing is rushing the slow, and the primary cause of that is not being strong enough to fully sustain the final quick. You can make the task simpler by not rising very much at all - but usually when people get ahead of the music, they rise more to try to slow down (making it waltz-like) and that just means they will have even more trouble with getting into the slow after that too early...