Should the Military award those who can Maintain a High/Max PT Score?

Definitely. I am personally think it's a waste of time having soldiers who are in top shape and able to get a 290 and above doing muscle failure when he or she can do that on his own. Also, this serves as an incentive for the soldier to continue exceeding the standard and motivate others to do the same as well. At the same time, it's important to occasionally have company with all the soldiers present to stimulate espris de corps. Other than that, SMs with high PT score should be awarded for their hard work and discipline.

I think so. Being allowed to PT on your own shows a unique level of trust from the unit leadership. It's a privilege most soldiers would be proud to have and therefore an effective motivator for soldiers to up their score. If soldiers are consistently getting 290 or above (there aren't many in most units) then they're doing something right. They're likely doing additional PT on their own to maintain that kind of score so reward them occasionally - once or twice a week. Why not?
But I agree with CPT Hermida that PT has a greater purpose and unit/group PT is essential on so many levels. Been in for over 20 now and many of you will understand when I say that some of the most vivid memories I have are of colossal group PT sessions...that time we ran 10 miles...that time we got lost while TDY at Cherry Point...the grueling buddy carries up "Cardiac Hill"...or that time my shoe fell apart and my squad encouraged me to keep going to the end...bloody toes and all.
Group/unit PT is critical to unit cohesion and individual leadership development. One of the things I love about PT is the fact that we're not wearing rank. PVT Snuffy can (and will) lead stretches or call cadence which might not ever happen otherwise. It's an opportunity to exercise leadership and put into practice ones motivational skills.
If someone has a bad PT day or falls out for some reason...they learn from it, others learn from it, and tomorrow is another day. In the end everyone goes to breakfast, puts on the duty uniform and switches focus...until tomorrow morning and then it's game on again! Group/unit PT really is essential to the Army experience.
But, I see no reason why soldiers that excel couldn't be rewarded once or twice a week for superior physical fitness. It's just one more method of rewarding soldiers for exceptional service and motivating others to do the same.

Thought we already awarded something for it! Isn't this badge of honor bestowed upon those who get and retain physical fitness excellence? I know junior enlisted and officers who receive Certificates of Achievement for promotion points from Battalion Commanders. Is there something more warranted for maintaining one's personal and professional physical fitness? How about living an extra 10-20 years and not becoming a couch potato? I think the Army does a good job recognizing it with a patch for the uniform for everyone to know who you are and then the one's who need the points, the COAs work. For mid-term careerist, well just being a professional is enough without the recognition.

I don't see why not. I earned 300+ if you can say that...I always earned above the 300 every 3 months for approx. 20 years of my career. I got 289 I think at basic entry and then 295 at graduation. Then it was 300 the rest of my career. Not to mention every time I had to go to schools. So yeah, why not an award? I worked very hard to keep it up and lead by example including going to Master Fitness Trainer School. I then had our Unit make a really good passing grade and higher moral and that I got an award for. But I didn't join the Army for awards but I think it helps one to keep striving when one is recognized for their strengths. I liked the patch we got to wear on our PT's if you got over 290. I remember Soldiers wanting to earn those. That is what I worked so hard for and wanting my Soldiers to earn for themselves and for the Unit and that meant a much healthier stronger minded and bonded Unit.

Sure, the award is being allowed to stay in the Army. It has been my experience that just because you are physically fit does not mean you are a good leader.
Take my situation for example.
As a brand new private E I owe you one, I was 17 yrs old, built like a pencil and a PT stud. Due to my PT abilities I was continually placed on a pedestal above my peers as though I were somehow superior to them. I had no idea how to do my job, no leadership experience, no knowledge of Army life, traditions, standards, etc... You get the picture. However I was viewed as top notch.
Now 26 years later, my knees are shot, multiple back injuries, deployment related injuries, and other age related ailments. I can no longer PT like I could then, but I have a quarter of a century of experience in peacetime and two wars. Referred to as extremely knowledgable, dependable with exceptional leadership skills. However no more pedestal, viewed very differently, passed over merely because I can't PT like the rest of them. Illogical?

A Soldier who can max his PT score does not need to do PT with his unit because what ever he's doing is working.
But if this Soldier happens to be a squad leader, that Soldier should be running squad PT with the intent to improve the squad's score.

Yes & No.
Unit PT serves two major functions. Physical Fitness Training and Unit Cohesion.
The first is to get people up to a higher level. The second is to make people a better team.
Allowing people to PT on their own potentially meets the first goal but is counter to the second goal, therefore a balance must be met.
Assuming that there are 3-5 hours of dedicated PT time on the training schedule per week, how much time can we reasonably remove?
That said, how much of that is actually used to progress? That would happen "off time" anyways.

I would disagree to reward anyone for meeting PT standards. That is just it, "meeting standards". In fact, I sometimes wonder why the Army changed their PT uniform from combat boots, fatigues and t-shirt to sneakers and shorts. Also, changing the PT Test from a 6 stage PT Test to a 3 stage PT test. Yes, I know that I will receive flak and hear that reasons for changing the uniform and standards were due to unfounded benefits of the other requirements and that sneakers were adopted to prevent injuries. Before you respond, I get that. But the first question you will need to ask yourself is: "Do we go to combat in sneakers?" Just my thoughts all these years and in no way to offend anyone.

They should be given the Army PT patch if they get a 270 or above with 90 in each event. In my battalion if you get 270 or above you get a COA and for 300 or higher they get an AAM (one within a 3 year period).

We used to give PRO PAY for those who tested high, why not PRO FITNESS PAY, since it too affects readiness?