There does seem to be a need gap in the current social analytics tools in the analysis of someone else's profile, from what you've said.
Although technically all the requisite information can be scrapped from the public data, the compute & storage to do so would be crucial. It's unlikely that a tool can pre-index all the Twitter, Facebook data and so it needs to be done on-demand. Even on-demand, the overhead is high that the tools limit the data to recent 100 tweets/posts as mentioned by you (at-least in their free version).
I came across personal twitter search tool - https://github.com/saasify-sh/twitter-search which uses Algolia and a SaaS hosting service; such similar setup can be a starting point for someone looking forward to address this need gap.