Disadvantages of playing a monstrosity depend on world-building and social acceptance
Monstrosities as a creature type are described in the Monster Manual (page 7):
Monstrosities are monsters in the strictest sense - frightening creatures that are not ordinary, not truly natural, and almost never benign. Some are the results of magical experimentation gone awry (such as owl bears), and others are the product-of terrible curses (including minotaurs and yuan-ti). (...)
A typical civilized society would not be expected to allow monstrosities, that is monsters in the strictest sense, in their midst. Such creatures would be persecuted, and authorities would try to arrest and eliminate them, as they would be seen as a threat to the safety and well-being of the population. This would make the character near unplayable in social adventures, unless they had a good way to hide their true nature. It also would make it difficult to obtain any kind of healing and support from temples or other organizations, and to find lodging or buy equipment.
None of these disadvantages are mechanical in nature, but they still are very real, and can make it un-fun to play such a character, even if the character race mechanically is powerful.
In older editions, drow were an unquestioningly loathsome, evil race feared by all good folk, but had powerful racial abilities like innate spell-casting. They experienced similar issues as player characters when playing drow (especially dual-wielding rangers) became popular due to the Drizz't do Urden novels.
Social disadvantages depend on the DM's interpretation how people will react to such a character, and on world-building. For example, Thri-Kreen originate in the Dark Sun setting where they were not uncommon, and in second edition were a playable character race in the Dark Sun setting, maybe somewhat distrusted, but not automatically persecuted.
Back in 1e, the DMG advised about The Monster as a Player Character (p. 21 DMG 1e):
The considered opinion of this writer is that such characters are not beneficial to the game and should be excluded. Note that exclusion is best handled by restriction and not by refusal. Enumeration of the limits and drawbacks which are attendant upon the monster character will always be sufficient to steer the intelligent player away from the monster approach, for in most cases it was only thought of as a likely manner of game domination.
In general, D&D has become much more inclusive and embracing of diversity, with things like Drow and even demonic-origin Tieflings a common character option even in the core rules. A DM following this trend may opt to disregard many of these disadvantages, and rule that there are so many weird creatures out and about, common folk in his world will not bat an eyelash at seeing a Thri-Kreen walk down the street or order ale at the local pub.
If the DM does not enforce social disadvantages for playing a monstrosity, then indeed, the mechanical bonuses may be pure upside.