I agree with what you said. The point I was trying to make (that probably got lost) is.
There are no different standards for 1st, 2nd, 3rd or 4rth Nikah. 2nd and later nikahs are allowed exactly for the reason the first nikah is allowed for and that is physical needs. Saying that islam allowed 4 marriages to support widows or divorced woman is not true. You can support them without marrying them. You dont have to marry them for that. Point is, you are allowed to marry a woman of any status (virgin, widowed, divorcee) for any of your nikah.