Should Senior Software Engineers do Project Management?

Hello everyone, this is my first post here which I wanted to start with a discussion which was the point of curiosity for me for many years of my work in IT. Here is the question: should senior software engineers do project management?
Let me give you some context here. My career path like many others started with coding only. Later it progressed to other levels where coding was becoming less and less of the main responsibility and in the end I had very little of it or not at all. Instead one of the main tasks of a senior technical lead person is to decompose business requirements into functional system components and provide an estimate and team recommendations to implement it. And this is where things start to be really interesting.
Think about it. The primary goal of any Product Manager is not just to understand the cost of the project but also the timeline of when it's going to be implemented. I had this question coming all the time from PMs and stakeholders. To build this timeline you need to be really well aware of technical specifications of the project, its dependencies and nature of work to be completed. Usually Project Managers don't have such insights so they ask developers to help with that. So major part of my work was building draft schedules and working on project design not just from technical but also from execution side of things. I even created an app which can automate this and hopefully help simplify this process in future (if you're interested you can check it out here ).
What do you think of this question? Should responsibilities of Tech Lead/Architect include partially the responsibilities of a Project Manager?