url rewrite to avoid third level domain still make sense?

"or for simplicity the third level domain remains the best solution?" - Yes 3rd Level domain is easy to understand and works great. However, since your business prefers the other way, rules to redirect the traffic based on URI is you have to go with.

"the url rewrite to avoid third level domain still make sense, is it still valid," - Yes it makes absolute sense and I find no reason why it should be deprecated. However, with the 3rd Level domain your could use separate VS with separate VIP for each 3rd-level domain name, which will not be possible now. So, it becomes a bit complicated affair to troubleshoot any problem with any particular URL, having the same domain name "company.com".

hope that helps.