i) What's the problem with asserting the perpetual virginity of Mary? The main problem with the Catholic interpretation is not that there's overwhelming evidence against their interpretation. The problem, rather, is taking pious legends for which there's no good evidence, or even some evidence to the contrary, then elevating those pious legends to the status of dogma so that Christians have a solemn obligation to believe it, on pain of sin or heresy if they refuse to submit.
It's bad enough to impose on Christians a duty to believe something for which there's no good evidence, and say that if you refuse to do so, you are guilty of sin or heresy. It's even worse when not only is there no respectable positive evidence, but there's even some evidence that the legend is false.
ii) To begin with, there's just the standing presumption that the "brothers" and "sisters" are biological children of Mary and Joseph unless we have credible independent evidence that it's not the case. Unless you already know that can't be so, there's no justification for viewing them as cousins. So there has to be good evidence to overcome that presumption.
iii) We also know that the early church promoted the ideal of celibacy and demoted conjugal relations. So that's one reason to view these legends as having dubious pedigree.
iv) In addition, if Mary and Joseph had a platonic marriage, that creates a theological problem. According to Catholic canon law, as I understand it, even if a couple is married in a Catholic church, by a Catholic priest, using a Catholic marriage ceremony, that's an insufficient condition to make them truly married. For the ceremony must be ratified by consummation. Unless the rite is consummated, that's grounds for annulment.
The theory behind annulment is that marriage is indissoluble, so annulment doesn't dissolve the marriage. Rather, annulment is an official recognition that there was no real marriage in the first place, because one or more necessary conditions were lacking. Applied to the case of Joseph and Mary, a platonic marriage would mean they were never really married.
The theological problem that causes is that according to Matthew, Jesus is the royal heir of David, but he can't be David's royal heir unless he's David's descendent, and he can't be David's biological descendent through Joseph since Joseph is not his biological father, so he can only be David's legal descendent through Joseph if Joseph is his stepfather. Yet on the Catholic interpretation, Joseph isn't even his stepfather.
Perhaps a Catholic would say the pope can waive consummation as a necessary condition for marriage in the particular case of Joseph and Mary, but that's an ad hoc exemption.
v) I'd add that there's a drastic asymmetry in this debate. On the one hand, Protestants have no real stake in this debate. Suppose Mary was a perpetual virgin. That changes nothing in Protestant theology. No adjustments required.
On the other hand, if Mary and Joseph had conjugal relations, that instantly falsifies Catholicism. It's a package deal. If any Catholic dogma is wrong, that single-handedly sinks Catholicism.