p. 190 Moving between attacks:
"If you take an action that includes more than one weapon attack, you can break up your movement (...)"
For this rule unarmed attacks are the same as weapon attacks. https://twitter.com/JeremyECrawford/status/608776737917263872
So splitting up an attack action or a bonus action is the same and very much in line with the written rules.
Also the extra attack class feature of fighters, paladins, monks does not give multiple actions. You still take one action, but can make multiple attacks. p. 72
In addition, monks are themed around self enhancement and bursts of speed through the use of ki, so letting them, as the only class that has multiple attacks within a bonus action, treat that action just like the normal attack action makes sense with the class fiction.