Sure it is, and we do, every year. But right after Yom Kippur we have
an immediate opportunity to start sinning all over again. One obligation
for the evening prayer that follows the fast is not to pray it at warp
speed. Innocent or guilty?
More seriously, it's a great question; I'm sure many other people wonder
about it too. There are three types of answers: 1) classic; 2) mussar
[ethical] 3) chassidic. Hereis a sample of each:
1) On Yom Kippur we seek forgiveness for our sins of the entire previous
year. In the night prayer, we are addressing the sins we did on Yom
Kippur itself. Sound farfetched? After all, we fasted and we prayed.
A lot! Well, there are some Jews that didn't each year, and the plural
phrasing of our prayers includes them. But even concerning us, one of
the faults we disavow in the Yom Kippur confessional prayer is false
confession. So if we weren't sincere throughout the entire confessional,
we have a problem!
(This may also apply to many of the shouters of "Next year in Jerusalem.)
2) Although we gained a stay from punishment, it does not necessarily
mean that the record and traces of the sin no longer remain. It only
indicates G-d's tolerance and patience. We still have to do further
tshuvah to guarantee that punishment will not be visited upon us at
some future date (in the name of R. Yeruchim Leivvitz of Mir).
3) Once, a chassidic Rebbe's son asked your question of his father.
The Rebbe's reply: "Now we really have to do tshuvah."
Presumably the Rebbe intended that once we have accomplished the basics
and gained forgiveness from punishment ('lower tshuvah'), we have to
move on to remove all negative imprint left by the improper deed, in
order that nothing interfere in our relationship with G-d, that it be
as perfect as possible ('higher tshuvah').
He also meant that due to our tshuvah and sincere prayer on Yom Kippur,
we grew to become better, more spiritually elevated persons, and as
a result, a deeper, more penetrating level of tshuvah is now required
of our "new," improved selves that couldn't really be expected
of the pre-Yom Kippur versions.
More simply, 'lower tshuvah' is for our own sake, based on fear; 'higher
tshuvah' is for G-d's sake, out of love.
4) In addition, there is always the straightforward, practical, Jewish
law reason to davenn the usual week-night prayer: "We do
not alter the coin which the Sages have minted."