In Poland, I've seen a real-life check only once in my whole adult life (past ~20 years). Any amount, literally from $1 to $10M+ is being sent by a wire transfer, and wire transfers cost $0-$0.25 flat fee, arriving within the same working day, or instant.
This is how it has worked for the past 20 years, and the more recent innovation is having a similar system working all across Europe, and instant transfers within the same country.
Depending on a bank's security policy, the only difference between amounts is that some banks won't allow you to send wires above a certain amount from mobile, and with some banks you have to appear in person for wires above say $50k.