I sense a fear of stablecoins among UK and EU regulators.
As an interbank settlement mechanism and the cash leg for blockchain transactions, however, they are a fine use case. Some banks are pushing for this and have developed solutions. What's missing is massive liquidity and established players; otherwise, this will remain a niche instrument. Banks won't agree to a cap on holdings.
On the retail side, regulators obviously cannot give way to stablecoins. They believe that stablecoins would give US payment providers more control over European customers, which would result in a loss of sovereignty. There are no noteworthy European stablecoin providers because none would be allowed to dominate the market.
Regulators are actively promoting the digital pound or digital euro as a tool of financial innovation and a European alternative to Tether, Circle, and PayPal. UK and EU retail customers presumably don't care about a cap on holdings.
Currently, there is no major need for a stablecoin.