So, why aren't there any Baptist monasteries? Is there some sort of theological opposition, or do Baptists just don't do it?
In general, Baptists have historically harbored animosity towards anything that smacked of "papistry." Note, for example, John Bunyan's polemics in Pilgrims Progress. Add to that a fear of turning the Gospel into a "work," and you will see that it definitely goes against the grain of traditional Baptist upbringing.
As always, with Baptists, nothing is universal. It's not that we "hate" spiritual discipline, it's just that it usually doesn't occur to us.. The same things that apply to mysticism and spiritual discipline would adhere to asceticism and monasticism too. Often after reading something by Dallas Willard a Baptist might get a notion to have a new "experience," but in the main the historical and theological norms would tend to discount the monastic impulse.