I tried ixwebhosting but I later found that they have a file limitation of 100,000 for Window's servers which is even worse than having a limitation on storage or bandwidth and is a lot more limiting. I'd rather have a limit on storage than a limit on file count. So really be careful with that company. I find it to be false advertising for a company to claim unlimited storage and unlimited bandwidth when they have a very limitating file limitation. I believe it's 100,000 files for WIN and 300,000 for linux. The good thing however about ixwebhosting is that their online chat service is pretty fast and sometimes helpful. But unfortunately, ixwebhosting will send you a violation of their TOS when they feel you have hosted too many websites and use the file limitation to try to make you upgrade to their VPS.

Just curious what kind of website that has more than 100000 files?
For now there is no hard disk with Unlimited GBs capacity yet, and no internet cable capable of unlimited bandwidth.
So whatever hosting package you pay for, keep in mind that a provider needs to host a number of customers on a server with limited harddisk and limited network connection.

Doesn't their TOS have over the top arbitrary limits such as "x MP3 files" and "y RAR files"?

100,000 files overall still is a very high number though. You should consider hunting for frivolous files and clear them out. If you have logging enabled and these files count, you could quickly reduce your file count. If you're serving downloads or keeping backups, try archiving them so instead they consist of 1 file.

It's not false advertising, you clicked "I Agree" to the terms when you signed up. They list the limits right there.