As everything it is a matter of individual taste.
And it is up to everyone to describe or rationalise it in her/his personal fantasy in every way she/he likes.
I definitely like my presents to be nicely wrapped. It offers so many possibilities to play, to tease and to prolonge the fun, which I usually prefer over blunt nakedness and quick satisfaction, although those have their place as well, from time to time.
Surprisingly I often found that the ladies (no matter whether mistress or slave) prefer slave girls to be naked, while men more often love a more elaborate presentation of the goodies.
In my DA galleries (for example 'NFC - the never finished Comics' or 'Kajirae from Rote Seide') you can find quite a lot of slave girl outfits and I never get tired to invent more of them.
Naked is going to happen, but being stripped, or ordered to strip myself, is also exciting ...
... usually I would expect, that if I'm in my 'normal' clothing, I'd be ordered to strip.
The 'loincloth' I feel is more of a part of the crucifixion ceremony ...
it's not so much for any 'modesty' of the condemned,
maybe for upholding a certain aspect of public order ...
- the fully naked condemned, is a social outcast
- they can be seen that way on the suffering-grounds, or inside the dungeons, or before the judge who decides their fate (the sentence should be spoken on a nude delinquent, I'd expect ...)
however while carrying their cross or patibulum through the streets,
where they're seen by the 'good people' going about their daily lives,
maybe a pretense of public decency is upheld,
and the view of the naked condemned wretch might be offensive and a kind of moral pollution.
In that way I'd see the loincloth more as a symbolic/ceremonial garment meant to identify the condemned while upholding public order ... when the punishment is carried out it's taken away.