Companies may also be registered at CH and not incorporated, as prescribed in Company law, so if the member was date_of_incorporation, that would be inaccurate and misleading. In this case, date_of_registration is better, but then we're faced with two member names which are mutually exclusive. Nasty.
We have taken a very deliberate and determined approach with members naming, so that when you read your own client code or look at logs, the member names are self-documenting. Our view is that documentation doesn't end with the Developer Hub!
The decision was therefore made to use a neutral member name for the date the company was created at Companies House. We did consider "start_date" and similar names, but they really were confusing, for the reason you give: the company my have started before it became a legal entity at Companies House.