Yes, I'll pay with coin and/or ask for change. There is no insult. ATMs often only dispense 20's. The woman wants paid, not have it tied up with a little red ribbon. Pay first = business. Nicey-nicey = what you do (if you wish) in the time you've paid for.
In practice, a sauna (parlour) can always give change (or is pretty shonky if it cannot). A better class of prossie with half a brain can and will realise that a punter may not always have the correct amount and have at least a small kitty of a fiver and a tenner. She's half way between an "exact fare only" bus and the personal service of a receptionist.
It's just a bit pointless to expect she will
have change as that puts you in the awkward position of getting some too late (which might fuck up her booking schedule, at your cost), or oozily giving it as an advance 'tip' (in the unrealistic hope, with an oozy smile, that she will appreciate it and add on a bit extra -- how the fuck would you know anyway unless it's part of her price list?), or arguing the toss and getting her to accept a lower amount (which is not very likely to happen).
As for coins, I detest it when a shopkeeper gives me a big pile of coins as it means I have to carry them around. But she doesn't (and she has a bloody fill-as-much-as-you-want purse & handbag for such things anyway). If I give coins for a large amount I try to give 1 and 2 pound coins, partly as I personally have an unpleasant association having to count small coins if given them and partly cos I don't want her to spend my fuck time counting small change. The worst scenario would be a momentary sigh as she thinks of her cupboard with wads of tens and twenties all neatly rolled up into 1K lots, or a held-back grateful tear as she imagines scraping it pitifully together and having enough to pay her drug dealer. Who gives a fuck. Your responsibility is to arrive clean and polite and pay the agreed amount. Hers is to arrive clean and polite and provide the agreed services.
It's not really a big deal.
Get over it.