If you happen to be part of a two person team without any money you're CTO is going to need to code. At a team of 4/5 the handoff begins by employee 11 they shouldn't be coding perhaps firefighting if necessary.
It's a joke to give yourself a management title when there's nothing to manage.
Being a 2 people company or a 20k+, you still have to manage financial, technical, operation aspects of your business.
Same role name, different implications depending on scale.
If you are a small handful of people starting off, you don’t need a CFO, you need a bookkeeper and an accountant. You don’t need a CTO, you need a tech lead.
All that rest is a mix of confusion and puffery.
Ignoring that when giving yourself a C-level title is what I take issue with.
Same role name, different situational implications.
Being a mayor of a small village or of Paris or New-York, you're still the mayor.
In fact, it's not even with the people you're directly dealing with where this becomes useful (as, if you're selling to Big Enterprise Client, you likely have a network inside the company anyhow). It's when the person you have a relationship with has to convince his/her boss to approve an invoice from your little shop.
So really there's no practical difference between a company of 11 people and a company of 11000 people from a management perspective.
The technological/practical concerns you'll be dealing with are totally different, of course, but as far as 'people management' stuff goes, there's little difference.