Doing a series H might make investors think harder about why they need 8 rounds of funding over 12 years or so and still didn't manage to turn a profit.
I had a recruiter a few years ago pitch me about an amazing opportunity at a series F company that he wouldn't name in the initial pitch email. I didn't see that as an advantage at all. That's 6 rounds of investors who are all going to need to get paid and then some before you see a penny. It also implied to me the early growth/fun stage was over and they either limping along or so big to be unrecognizable as a legit startup.