The problem is, we do not need different services using different formats all over the place. I see with the latest Bitcoin Core 0.16.0 that was released, they sort of singled out Bech32, so I reckon that is the way things are going to now.

This means I have to switch to wallets that use Bech32 or hope that my wallet provider makes the switch soon.
I wouldn't phrase it as 'singled out'. By default Core 0.16.0 will give you a '3' Segwit address and you have to specify if you want to have a bech32 address instead. The most important thing is that Core will now let people send to bech32 addresses. So hopefully, that will lead to all the services allowing withdrawal to all address types and everyone will be able to choose which they use.