So this is a Pre-Allopathic forum question, not Allopathic. There are more readers there that are better suited to answer you question.
Answering your question, EMT is not as helpful as pre-meds make it to be. It's not to say that it's hurtful, but it's a totally different career path. EMT is not meant to be a precursor to medical school. It's supposed to be a precursor to Paramedic school, and not only does your training have a totally different thought process in terms of how you should think of things and your role in the healthcare delivery model, you are potentially taking away a spot from an EMT who actually does want to make a career out of it.
Thinking that it will help you in your physical exam skills so it must be a good idea is short sighted. Number one, you don't need a head start. Medical school is structured to thoroughly teach you the physical exam without any past experience. Moreover, many other areas of your training are likely to suffer as you will likely think, oh I know this, I learned it while I was an EMT, I got this, move on to someone else. However again, the way a physician thinks and does things is different than an EMT, and the only thing worse than a useless M3 on rotations is a useless M3 who thinks they aren't [useless].
Also, scribing isn't "invaluable". I was a scribe, it's fun, it's useful in gaining some comfort with drug names/diagnoses(what they mean, not how you arrive to them), proper note writing form etc, and more importantly it looks nice for medical school but if your biggest take away come interview time is, "well I really feel like I gained invaluable insight into the thought process of a physician" you are going to tank big time during your interviews.
Lastly, let me repeat. This is the wrong sub-forum for this and should be asked/moved to the Pre-Allopathic forum where you have a better suited readership to answer this question.