Why were Muhammad's wives not allowed to remarry

[Amra94]

33:53 ...And it is not right for you to annoy the Messenger of Allah, nor ever marry his wives after him. This would certainly be a major offence in the sight of Allah.

What are some good reasons for this prohibition?

[good logic]

Sister,
Like 4L22, not marrying women who were previously married to our fathers. Nor can the father marry the divorced wife of his genetic son (4:23). This divine prohibition preserves our respect for our fathers and their most private affairs.

Likewise, 33:53 applied to the believers during his time and that generation  after he departed. 
GOD bless you.
Peace

[hawk99]

33:53 ...And it is not right for you to annoy the Messenger of Allah, nor ever marry his wives after him. This would certainly be a major offence in the sight of Allah.

What are some good reasons for this prohibition?

Peace Amra94,

The wife of esteemed individuals is best remained private to show respect and to not impinge on his legacy.

God bless you.