Yes, although a person should only make use of this if they do not know how to recite the Tefillah themselves.
The question would now be whether or not there is anybody who is unable to recite the Tefillah themselves given that it can be recited in any language you understand (or in Hebrew even if you do not understand, such is the special nature of praying in Hebrew, although you are supposed to understand the first b'racha, and the general nature of what the rest of the prayers are about).
With readily available translations into native languages, it is likely that anybody, even who does not know Hebrew, could pick one up and pray themselves.
We always have Chazarat Hashatz because it might embarrass someone if you ask publicly whether there is any individual present who needs it. Also in order to recite the Kedushah prayer and whenever Birkat Kohanim is required and also, I suppose, in case (and this probably applies a lot) anyone who did recite it themselves did so with inappropriate kavana and needs to repeat it anyway.
Where does it say you can just opt to rely on the Shaliach Tzibur?
What is does say is:
An individual who was unable to recite it (or who omitted part of it; see 124:10) fulfills his obligation by listening carefully to the leader; see 114:1-2. Even those who recited it individually should listen and answer "Amen" after each blessing (see 124:4-6); for other laws about answering "Amen" see 124:7-9,11-12.
Note "who was unable to recite it".. I haven't got what 124:10 but it says part of it, not all of it, and I assume it means he accidentally left out Yaaleh Veyavo or something else he should have recited, and it was b'di eved not l'hatchila