He looked the best of the brothers (he was the youngest) so he could play the romantic lead if nobody else had the role (like Oscar Shaw did in COCONUTS). However although his appearance was better than the other three brothers, he was not a really handsome man like Robert Taylor or Tyrone Power. Also he had a serious problem with his sense of humor - he had one but it was remarkably similar to Groucho's.
In fact, during the Broadway run of COCONUTS, Groucho was ordered by a doctor to take a long, overdue rest. He took off for two weeks, and was replaced by understudy Zeppo. At the end of two weeks he talked to the producers, and they willingly allowed him to take an additional week off. In fact, when that was finished they said he could take more time off if needed. Suspicious, Groucho went unannounced to the theater one night, and watched Zeppo being so good the audience was laughing hysterically at his delivery and acting.