Bandwidth costs are tiny, but phones use radios and radios cost lots of energy to handle real TCP connections that must be maintained. It'd drain the battery really fast. Plus it's a very rare telco indeed that gives your phone a real routable ipv4 address. Most are behind carrier network address translation.

But the spirit is right. Just do it on a real computer at home on a landline. A static website is easy, incredibly safe (compared to, say, browsing with JS turned on), and useful.