I wouldn’t word it that way (you pin it on the paucity of “daddy’s bank account”, but you could just as easily have blamed it on his not having a job), but no, I don’t think it’s responsible to get married without some type of reasonably realistic means of support. You do?
By “reasonably realistic means of support”, do you mean obtaining the means to pay for one’s needs, or obtaining from others the means to pay for one’s needs? While I certainly agree with the former (which can be realized via some combination of a job (even unskilled), chassunah funds, student loans, etc. together with being Mistapek B’Muat), there is no reason why the latter (including the Shver’s bank account) should be in the mix as a necessity or a requirement to get married.