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The shower before a pool is to ensure people aren’t entering the pool coated in dirt (e.g. sweat, hair, dead skin, etc…).
The chemicals in a pool are designed to bind to that dirt and kill any bacteria introduced.
There is a limit to the chemicals you can add to a pool (before it hurts humans) and once the amount has activated you need to drain the pool and refill it.
Swimming pools hold crazy amounts of water which is also really expensive to heat up, so pools want to do that as little as possible.
Clothing interfers with cleaning your body, so people entering near fully clothed (e.g. like a Burkina) will likely introduce more dirt into the pool.
That translates into increased costs for swimming pools or pools which maintain the old schedule and just operate unsafely.
This is all based on owning a hot tub and learning how to maintain it.
Hopefully this also explains why it doesn’t matter people enter the sea fully clothed
You seem to be intentionally missing the point, but to reiterate…
You shower before entering a pool to wash the dirt from your body off (your cleaning yourself).
The more of your body covered the less effective that shower is.
Ideally everyone would be naked in the shower, but there are probably outfits which increasingly render the shower less and less effective (e.g. speedos are better than shorts, etc .).
It would not surprise me if a Burkina covered so much that the cleaning shower is rendered pointless