No, the university professor age shouldn't be considered the reason to stop him/her from continuing education and research in academic institutions. If s/he desired to continue research activities, they should be encouraged to keep continue.
Thank you for starting this discussion. To my mind, that is a two-edged sword. On the one hand, one should mind non-discrimination principles. On the other hand, we are valued by our employers according to the value we provide. Since nowadays there is a trend to research universities, so a research productivity is mostly considered.
And in this respect, I came up with 2 papers I recently read.
Article Research productivity by career stage among Korean academics
and Research creativity and researchers' age (in Russian, but Google Translate might help, I believe) https://elementy.ru/nauchno-populyarnaya_biblioteka/434504/Nauchnoe_tvorchestvo_i_vozrast_issledovatelya).
If I got that right, the thing is not in the age, but in the productivity stage that might not correlate.