What is your format?

If it's 35mm, the recommended grade for 'normal' is grade 3. This
allows you to reduce the film development a little, which provides
better sharpness and finer grain.

Grade 1? No way.

Several potential pitfalls come to mind.  Not in any particular order:

1.  Availability, low demand for graded papers in general and especially
lower contrast grades may leave you without a source for your "standard"
paper overnight.  Most people use normal grade and use higher grades to
"rescue" images that are underexposed or otherwise low in contrast.

2.  If you use the lowest available contrast paper for "normal" images where
do you go if you need to print a higher contrast image?  What if your
targets and technique are calibrated for normal rendering of scenes of
normal contrast and you get pushed into a situation with high contrast
lighting or scenes with only a limited contrast range.  e.g. Stage lighting
(no lower grade paper to render a higher contrast negative) or "available
darkness" lighting in a bar where you need to push process film to get a
reproducible image.  If your "normal" film processing is already high
contrast you have nothing left in the way of extended development to "push"
process film.

3.  If you are processing negatives to a higher contrast the transition
between tonal values is sharper and you will feel the need for half grade
(or less) increments in paper contrast when printing.  The danger is that
some values may "block-up" and be unprintable without using variable
contrast paper developers or a lot of burning and dodging.  And frankly
variable contrast papers are easier to use than variable contrast
developers.

4.  Processing negatives to higher contrast encourages graininess as well.
Not bad in itself but needs to be considered especially if you use 35mm.

5.  By design paper grade 2 or 3 papers have contrast curves that fit the
contrast curves of standard films.  (Note that paper grade numbers are
rather arbitrary even in the product lines of one paper maker and that
contrast varies with product and shelf time.)  As a rule if your personal
aim points for contrast and exposure shoot for the middle of the field the
occasional unforeseen variation (or in my case a genuine screw-up) will
still keep me in the comfort area.