Actually, you can expect them to use a dynamic fee structure that allows users to choose their own fees. A few sites are starting to implement this. Some wallets already have been for a long time. There won't be a perfect system but better control over your fees should anyway be something wallets must look at.
Dynamic fees or not, there will always be a base minimum that exchanges and services think they need to cover the standard transaction fees, plus they obviously want their cut as well. Just out of interest, name up a few of these sites and wallet services that happen to use dynamic fees?
Counterwallet lets you choose based on priority and/or set your own fees, with a base minimum that changes depending on network and size of your tx. It's not perfect but it's a start.
Electrum lets you set a dynamic structure, a fixed one based on sats/byte or even manually - with a current low base fee of 3,000 satoshi. This base fee seems to go up and down, as I noticed. It even used to be as low as 500 satoshi (and from old versions I read even 0 fee was possible). My favourite wallet. This has always been a feature for as long as I've used Electrum.
Sites? Since June:
Localbitcoins uses dynamic fees.
Crypto-games.net lets you choose a fee structure based on sats/byte.
So yes, wallets and sites need to get on and keep up.