Nah, readers need some room for choreography. Leaving out those directions is a good start. However, there is an exception. If the direction is crucial and has been built up throughout the story, leaving it out won’t be a good idea. For example, you write a boxing story, and MC’s signature punch is a left hook. If you leave out the direction, the impact may not be as strong.
Take a boxing slugfest as an example. Of course on TV, it’s fun to watch, but in the form of written words, it drags the pace way too much.
The most important thing in writing action is that readers can never imagine how the fight exactly plays in your head, so don’t ever get too specific about the choreography. Just give them a gist of how the moves look like; they can fill the gaps by themselves.
If you read articles about writing action scenes, most suggest that you focus on the emotions and not the choreography because readers hardly care about it.
Also, get visceral. The spraying blood, the crunching bones, the pain, the stench, etc. I draw inspiration from Berserk manga (those two-page spread of carnage) to get as visceral as possible.