It is primarily a regulatory issue - an EU directive required countries to introduce a modern 'faster payments' system that realised the potential of electronic banking systems to rapidly transfer and clear money betweeen accounts. (In the UK the implementation of the regulations sets a 2-hour limit but in practice transfers are essentially instanteous). These are generally free for consumers but businesses will pay a transaction fee (a few pennies) which is the same as exists under the old cheque clearing BACS ("Bankers' Automated Clearing System") that took 3-5 days. BACS is still used for a lot of routine payments.
There is still a same-day 'wire transfer'-type system in the UK called CHAPS ("Clearning House Automated Payments System"). This costs c £20 per transaction and is still necessary for payments larger than the Faster Payments limits (usually > £20-50,000/day).
This situation is broadly the same across EU members thought the charging model may vary a bit, though one of the EU requirements is that banks charge customers the same for intra-EU payments as for at the same cost as intra-country payments)
Before they were forced to introduce 'Faster Payments' the banks resisted making changes, perhaps because they would get c. 3 days interest on the volume of transactions they were processing, but also because they were all largely dependment on ancient legacy systems written in things like COBOL that ran on an overnight batch-processing model and which they were terrified of breaking. Besides, it would not have been easy to get voluntary agreement from even just the main clearing banks on all the commercial and technical requirements.
In general, the USA's fragmented banking system is generally behind the rest of the developed world on banking systems. For example, by the time the USA was just starting to roll out Chip-and-Pin security it was near universial in Europe and large parts of Asia.