I like that thought and preach by the instructor
As most often you see new riders "walking" to their board in shallow water, and practising body drag now and then "only", but never when it is REALLY needed, and not like a normal thing for most sessions.
And suddenly when out deep, they fail to be able to retrieve their board, or get tired (or cold if winther) so their technique (which was "weak" in the first place) will not be sufficient
So I really like the idea of teaching to do it almost "always" when on the learning curve - as it is IMO the most important skill, that HAS to sit well on the backbone
I have no idea about how to cope with mud/low water though...
Besides that - many think that current is an issue - it is NOT !
Only if you have very freak currents in different directions, but hardly the case and extremely rare.
So no matter if you have strong current upwind or downwind or sidewind - you and your board will drift with the same speed (+ the wind at your board will make it even easier sometimes, but not always as you've seen yourself) , so it does not matter if current or not
You did the very right thing, as said - patience, thinking about it, and finding the solution yourself.
When you get more experienced, you can stop bodydragging if low water of course - as then you have loads of "routine" bodydragging upwind in deep water.
But for now, I think it is awesome that you practice in shallow water where you feel more secure and can take a rest.
(unless it is deep mud and impossible to stand/walk)
Although, if TOO shallow water, you can not bodydrag efficient - and you should just walk instead IMO.
I think the limit (with steady ground) is about "lower" waist deep, where you can easily bodydrag.
Whereas lower than this, approaching knee deep, is not easy or not possible
Welcome to a great sport !
PS: As written often - the MAJOR error done by most to start with, is pointing upwind with your arm - almost trying to "reach" for your board !
This is the correct way to go upwind when riding on your board - look and point "upwind" and the body and board will follow.
But when bodydragging in the water it is completely wrong, and you have to think "go sideways" halfwind, instead of "reaching up" for your board - and WHAM, now you will find yourself going upwind in the water like a rocket, instead of "stalling" yourself so to speak.
Try it, it really works