Actually a lot of companies will be able to provide that - just do not hesitate to get in touch with them and ask about such things. That is a mistake I think when people believe there there are only a couple of companies which will be able to satisfy their demand.
That's bullsh-t. There is reliable free hosting out there. Not all support WP and cPanel, so you really have to search harder for them, but I found some that are good. Google's AppEngine for example, is the best hosting there is, that is if you don't use Wordpress (since it's Java-based).
If your WP site got a large audience then I do suggest that you go with a host that offer WP hosting or get an openvz vps or if that does not satisfy you then go for xen. Image hosting is suitable to be host on vps or dedi i would recommend a dedi if you have a well planed on how to gain profits from it. Like others, I would say there is no unlimited disk space but some host offer unmetered bandwidth tho u might get some complication later but yet this is possible via shared port.
Another side note is that any "decent" provider isn't going to allow un-metered/unlimited disk space and bandwidth for a mere $10 a month.. However, I'm sure that a decent plan within that budget would easily suffice unless there are strict reasons for such massive consumption..
All hosts have CPU and RAM limits, otherwise a single user would be able to monopolize the entire server's resources.