Re your last sentence. As a lady who rode side-saddle for the last 25 years of 60+ years of riding horses, I can tell you that - done properly - one has a groom or gentleman friend to take the lady's hand (or if you were a bit "fast" you'd let them hold your waist) while one jumped down. Sadly, I didn't have a groom or gentleman to hand so I had to hold on to the saddle and jump or as I got older, I slithered down.
Apart from the elegance of riding side saddle (and as a surprise to those who've never tried it) it's much safer than riding astride.It's virtually impossible to fall off unless your horse falls in which case the safety . An obliging horse is an essential - although my Grandfather used to train difficult horses on side saddle because he was less likely to be dumped on the floor if the horse got nasty.
In the days when ladies rode horses either for hunting or riding in the park they usually rode a mare. Nothing to do with sex - just that mares tend to have longer backs and suits a side saddle better than a gelding - the side saddle sits further back than an astride saddle.
Of course men used the mounting block as did unaccompanied women. You noticed I said "unaccompanied women". "Ladies" never rode alone without a gentleman or a groom but "women" (and girls), the wives and daughters of farmers, well-off shop keepers et al) would be allowed to ride alone on family or business errands locally.
Sadly, my horse died 3 years ago and at my age and decrepitude I don't feel able to take on another horse.