But there is unrest brewing in the empires. The people are seeing democracy and how it alters things, in Europe and Canada and such. They are getting upset with the inequality of the absolute monarchies that rule their empires - and there is grumbling on the streets.
These highly educated emperial monarchies realize that they are facing an untenable situation. They'd seen what happened to the once mighty Tsar's for example - and they do the smart thing. The empires begin to transform into constitutional monarchies  - rule by parliaments with the monarchs every more relegated to purely ceremonial roles and freedom and democracy tbe law of the land.
In other words - they copy the British model because it's much better to end up like the British royal family than the French one. By taking these steps they hold on to much wealth and some power, before losing everything.

An Africa that only ever dealt with Europe as trade-partners would be a place Europeans beg to be accepted in for asylum