Ki abilities + beast shape + unarmored defense/movement (beastform counts as unarmored when it doesn't have natural armor, Monk passive translates over) = naked (ambushed while resting, etc.) hyper sponge tank build.
"You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so." Some of this might be open to DM interpretation, and I've read a lot of different DMs giving out different rulings on Beast Monks. An Ape or some such would probably be the most appropriate for some of the abilities. But you shouldn't get the unarmed strike in most situations since beasts usually use "natural weapons". Overall, this would probably be useless in a party full on barbs/monks/fighters, but effective with a team of rogues/glass casters.
BUT. Back to the original point, there are plenty of (better) multiclass options out there that don't detract heavily from your progression curve:
Improved Crit for a L3 ChampFighter on a Half-Orc Barb, plus action surge etc. makes for absolutely ridiculous crit-blasting.
Paladin main with a couple levels in Warlock bumps your spell slots for Smite output and gives you an easy range option (unlimited Eldritch Blasts, forreal?)
Rogues and Warlocks are just generally decent multiclass dips for offensive characters with strong arrays, but utility/support-minded characters might pick up Bard/Cleric for a bump if your party is too soft.