It has never been possible to apply for a visa at the border. Previously, if you were a non-visa national, you could show up at the border and prove you fulfilled the requirements of the Entertainer Visa, and be admitted on that basis. The Entertainer Visa has been rolled into the Standard Visit Visa, and the same is still true. Non-visa nationals can show up to the border and present evidence that they are carrying out "permitted activities".
From the UK government guidance for artists and entertainers:
Non-visa nationals can arrive at the UK border and provide documentary evidence to satisfy the officer that they meet the requirements of the route.
If you are a non-visa national, there is no difference in the evidence required, and the permitted activities between applying for a Standard Visit Visa in advance, and presenting yourself at the border. Hence, if activities were previously covered by an Entertainer Visa, and you are a non-visa national, it is still permissible for you
to arrive at the UK border without a visa. You will not technically receive a visa, but this was also the case before the Entertainer Visa was abolished.
As a US passport holder, you're a non-visa national, so you are entitled to prove your suitability for admission at the border, without a visa.