Is living with constant mindfulness necessarily good? or does it limit one's potential? Isn't mindfulness is difficult for a thinker which usually philosophers are?
Mindfulness by definition is bringing awareness to present moment non judgmentally and I agree it may relax you. I believe it happens because you shrink your attention to such a short span, in a moment by moment fashion that complex thoughts can't be formed and thus you relieve yourself from any unpleasant (or pleasant) feeling that may arise from complex thoughts. In simple words, you reduce your suffering, if any, to at it's minimum by limiting input to senses.
However, is avoiding complex unpleasant thought always desirable? aren't these thoughts and their uncomfortable feelings motivates and inspire us introspect and change?
For example: In early childhood I had my belief and respect for patriarchal social system(disbelief in gender equality). It were some uncomfortable thoughts that made me correct myself and disregard such systems which causes unnecessary man made suffering. If every time I felt uncomfortable and practiced mindfulness to avoid them, I might passively be supporting such system till date.
You may say some thoughts are useful and worth attention &amp; others not. Like worrying about upcoming college exam won't do any good, you may just use best of the time left. However can we say that with 100% certainty? The worry is something bringing your attention and focus to a problem at hand, may be you could be one in a million who will get a brilliant idea to handle such situation or device a undetectable way to cheat, or it may just help to focus and put 100% to prep for exam or it could keep you panicking, unproductive and prove itself a useless thought pattern. Similarly if you fail on an exam, there is no good in being sad about it or is there? may be the sadness is useful in making a neural pattern in brain to put more effort and time next semester.
Hence I even find judging thoughts worthiness is difficult and inconsistent. However if you are having too many negative thoughts keeping you on the edge on a regular basis may end up in health issue, in which we can regard it as certainly a problem.
To summarize, wouldn't being too much mindful may make you too adaptive to be mal-adaptive? wouldn't it may stop your thought processes which might have produced some good for society? and wouldn't it limit your potential.
Mindfulness by definition is bringing awareness to present moment non
judgmentally and I agree it may relax you. I believe it happens
because you shrink your attention to such a short span, in a moment by
moment fashion that complex thoughts can't be formed and thus you
relieve yourself from any unpleasant (or pleasant) feeling that may
arise from complex thoughts. In simple words, you reduce your
suffering, if any, to at it's minimum by limiting input to senses.

For me it is the opposite. In order to stay mindful and present you need a very stable and extended attention span. Philosophy, or just thoughts in general, are just mind wandering, it requires no effort, and no stable attention. And it changes nothing in reality. It actually limits your senses, mindfulness heightens your senses, because you are actually observing more input then when you are mindless.

However, is avoiding complex unpleasant thought always desirable?
aren't these thoughts and their uncomfortable feelings motivates and
inspire us introspect and change?

What thoughts are you talking about? The content of the thought does not really matter, what matters is how you react to it. You could have thoughts about strawberries, but if you are allergic you may react in a negative way to them (resistance), if you love fruit you may react positive, and else just neutral. You can live on basic hedonistic principle if you want.

If every time I
felt uncomfortable and practiced mindfulness to avoid them, I might
passively be supporting such system till date.

Mindfulness is not about avoiding anything, it is the opposite, observe the present with as much attention as possible, but without reacting to it. That means to observe thoughts as well, but not react to them.

You may say some thoughts are useful and worth attention &amp; others not.
Like worrying about upcoming college exam won't do any good, you may
just use best of the time left. However can we say that with 100%
certainty? The worry is something bringing your attention and focus to
a problem at hand, may be you could be one in a million who will get a
brilliant idea to handle such situation or device a undetectable way
to cheat, or it may just help to focus and put 100% to prep for exam
or it could keep you panicking, unproductive and prove itself a
useless thought pattern. Similarly if you fail on an exam, there is no
good in being sad about it or is there? may be the sadness is useful
in making a neural pattern in brain to put more effort and time next
semester.

Worrying is not a single thought. Worrying is when you react to fear with fear. It creates a cycle, a loop of fear. Just observe the thought and the sensation you label fear, but don't react to it. Worrying doesn't help you focus, it is a distraction. It does the opposite. Yes it might get you so fearful and anxious and nervous that it makes you do something, but the result will not be of the same quality as when you do something calm and with full focus.

To summarize, wouldn't being too much mindful may make you too
adaptive to be mal-adaptive? wouldn't it may stop your thought
processes which might have produced some good for society? and
wouldn't it limit your potential.

If you get to that state of awareness of a zen monk where you have no thoughts at all, you would realize that society is just an illusion. How would you even be able to help someone if you are not mindful? If all you are aware of is your thoughts, how are you supposed to notice someone who needs help. What does it even mean to 'produce some good'?
Thoughts limit potential. Thoughts are limited and limiting by nature. For example if you believe that a snake will kill you, you will stay away from snakes, and potentially never find out that their venom cures cancer (just an example). Or if you believe that slavery is something barbaric and could never happen in the modern world, you could become a slave and never realize it. In yoga and buddhism this is called karma. Thoughts that skew your perspective and make you only see reality from a specific relative perspective. If you want to learn more, I recommend this talk from david bohm, a theoretical physicists