I've replaced some old switches. However, after replacing one switch
for the basement staircase (originally 3 way switch with common written
on the back) ... I replaced it with a new single pole switch.

Now if you're at the bottom of your staircase with no lights on
(whatever the reason) you have to walk up the stairs to turn the lights
on (or vice-versa). Am I correct?

Generally people need to have a means to illuminate their immediate
area rather than go stumbling around in the dark to find a switch.
This is the reason for three-way (and four-way) switches. They are
installed to have a means to turn the lights on in a space with more
than one entrance. They also can typically be found at the tops and
bottoms of staircases for the same reason, as you can see.

Or if your dwelling is really older than maybe you should consider
intalling them in this manner.