Mechanically, within the radius of their blindsense, a blind character functions as a character with normal vision, with the benefit that nothing can obscure their vision.
Within that radius, this makes them stronger than creatures with darkvision standing in darkness. They are immune to the effects of spells like fog cloud and darkness (and of course, spells that cause blindness), and their opponents gain no benefit from effects that render themselves invisible.
Outside that radius, everything is heavily obscured and opponents have the benefit that they don't need to use those spells or effects (conserving resources). The character has disadvantage on attack rolls against opponents at this range, while these opponents have advantage on attack rolls against the character.
By focusing on melee combat (unarmed strikes) the monk is able to take advantage of some of the above benefits simply by staying close to the enemy. Even deflect missiles, since it doesn't depend on sight1, works as normal, mitigating some of their weakness against ranged attacks. In addition, the Way of Shadow monk will be able to cast darkness without hindering their own "sight". Even the Way of the Four Elements monk is not significantly limited, as very few of their "spells" rely on sight.
All in all blindsight is a decent way to wave off the mechanical disadvantages of blindness, and a clever player can even take advantage of some of the above benefits. I would advise against including tremorsense though. If you look carefully you'll see that is specific to burrowing monsters. Blindsight alone, even limited to 15 ft., is sufficient for this build.
1. As @SeriousBri points out, features that require sight will say "that you can see"; compare the Hunter Ranger's uncanny dodge.