There is a plugin that implements some of what you are proposing,
tagselect.vim, "Provides a better :tselect command," by Hari
Krishna Dara. It was last updated on June 9, 2005.
https://www.vim.org/scripts/script.php?script_id=1282
It provides the same display of tag information as :tselect and
related commands do, but in an easier-to-use menu. I have Ctrl-]
mapped to the :Tjump command.
It could use some updating. I think what you propose is a good
idea. I'm not sure that it needs to be incorporated into Vim if it
works well as a plugin. That is, if it's not missing some
functionality or performance that it would have if made part of Vim,
then it's probably better to leave it as a plugin. For one thing,
a plugin is easier to modify, so it is a better medium for proposing
new functionality than changes to core Vim.
If the functionality was to be added to Vim, I don't think there is
a need for more commands. I think users will prefer either your
interface or the original, but will probably not switch between the
two. Therefore, I would propose an option that let the user choose
between interfaces, perhaps with choices of legacy, Hari's style
with the menu in a split window, and your style with the menu in
a pop-up window.
On the other hand, having an option that changes the behavior of an
existing command could break plugins that use :tselect and related
commands. So maybe it would be better to have new functions that
the user can map, although that's not as convenient.
My rambling $0.02.
Regards,
Gary