Those profiles would quickly become so broad as to be useless. Context in the moment is the most important thing, which is why even Google shows ads targeted to your actual search query.
Cookies are also not an identity and refreshed very often. Their main use is to cap ad frequency and track conversions over the short-term (hours to days).
Google and Facebook do not provide any personal identifiers. That would be a massive breach of their core 1st party dataset. What little data they did provide is now gone with GDPR.
