I know a lot of companies where the executive puts the expenses on their own card and then files an expense report at the end of each week.

In fact, even as a non-executive I'd have no problem putting SaaS on my points earning personal card if I trusted that my expenses would be reimbursed in a timely manner.

I've gotten multiple free flights and hotel rooms this way.

I might get down voted a bit because people could argue that the company should reap the rewards from any points but I don't personally see an issue with it.