The danger of large address space networks, isn't so much to the switches, themselves, but to the hosts. This because broadcasts need to be examined by every host to determine if it's something the receiving host needs to be concerned about. This is also a little bit true with some multicast too, although to a much lower degree, especially if IGMP snooping is active.
Another concern, with large address space networks, you're often more likely to "spread them", across multiple interfaces, that host the SVI to access layer devices. This creates the potential for other issues, especially if using dual links to the downstream access layer from different distribution devices. (Suggest you research unicast flooding, if you're unfamiliar with the topic.)
That all noted, yes in an IP environment, with hosts that aren't too broadcast chatty, you can often "safely" go larger than a /24. (BTW, there are IP environments where even a /24 is too large.) However, the classic /24 (or olde class C) address block serves fairly well in most cases. So, you should very carefully review the need to have larger address host networks. (BTW, one current exception is wireless host networks, which depending on the technology might "safely" go even larger. [We've used /20s for some of those, w/o issues.])
