In the pre-internet-banking times, you would just fill out one of these forms [0] to send money from your account directly to someone else.
[0] https://de.m.wikipedia.org/wiki/Zahlschein#/media/Datei%3AZa...
The high penalties (historically) for writing bad checks meant that if you had a signed check in hand, you had at least a small level of confidence that you had actually been paid the money, much like cash in hand (it could of course be counterfeit, but you can assume to some extent that it is not).
Which parts of Europe? I use them all the time in France. A bunch of taxes companies have to pay can't be paid by credit card. It's either check or bank transfer.
Everything is debit card, bank transfer or MobilePay. Creditcards are only really used for travel and payment of US companies.
Apparently there was a Eurocheque system that enabled guarantees for international cheque payments in the EU but ended in 2001. This is generally cited as one of the main reasons cheques rapidly became irrelevant given that EC debit cards were still available and online banking became a thing.
Add to that that snail mail is still the main way people who ask for money communicate with you, so now you'll have to type in the IBAN by copying it from a piece of paper. The IBAN is also not authenticated, so you don't really know who you're transferring money to.
This may vary with the banks, but in some cases their website is horrendous. It's the case for my bank, BNP Paribas. I very much prefer to write a check and send it over snail mail if it means I can limit my use of their site.