Why should entrecôte meat apparently be cut into slices before served?
To directly answer your question - you slice it for presentation.
Entrecôte should be cooked at as high a temperature as you can achieve. This will tend towards charring the outside before the inside is cooked. As you should serve it towards medium rather than rare because of the fat content, you want to avoid over-cooking by doing it too slowly.
You are correct in allowing it to rise to room temperature before cooking. Some people would also salt it 30 - 45 minutes before cooking [others would object to that - your call, experiment]. If it was vac-packed, definitely allow it to come to room temperature between towels to help dry it out.
Once it hits your pan or grill, it should really only need a couple of minutes each side; this should be fast enough that it doesn't swamp your pan before each side is done.
After that, you either leave it to rest for at least 10 minutes, or place in a slow oven, depending on thickness. This is to allow the temperature to equalise &amp; finish cooking the inside.
Because it is heavily charred on the outside, for presentation you slice to present the tender inside as it's served.

Image is waygu, but best I could find royalty-free. - https://www.dreamstime.com/modern-style-barbecue-dry-aged-wagyu-entrecote-beef-steak-lettuce-tomatoes-offered-as-close-up-design-plate-image194816166