TL;DR Yes, sometimes. However, in general 13C data is much less useful than 1H (and 2D) data and the truth is we can often do without it.
I will limit my answer to the context of organic chemistry. Firstly, I directly answer your question: is 13C NMR ever used instead of 1H NMR? The answer is, yes.
However, I can only think of one case where one would do so. This is when there is severe peak overlap in the 1H NMR, such that one cannot reliably use it to ascertain whether one has (for example) a mixture of compound, or just a single compound. In such a case the 13C NMR (which has much more dispersed peaks and hence nearly no overlap) is more informative than the 1H NMR. This is generally not very common.
I want to go beyond a direct answer, though, and talk about the usefulness of 13C data in general. You are correct about the 1H NMR being more helpful than the 13C. This is generally true, and the main reasons for this are twofold:
13C NMR simply does not give as much information as 1H NMR. The only useful thing that one can obtain from the 13C NMR is the list of chemical shifts – but in turn, these are virtually impossible to interpret for all but the simplest molecules. On the other hand, 1H NMR gives you information about proton environments (shifts), number of protons (integrals), and limited information about molecular connectivity (couplings).
As porphyrin wrote, 13C NMR takes significantly longer than 1H NMR, because (a) the natural abundance of 13C is much lower (b) the gyromagnetic ratio of 13C is smaller.
As such, out of all the NMR data that organic chemists collect, the 13C NMR is by far the least useful and most time-consuming spectrum. On its own, its only real use is to provide a "fingerprint" of the molecule, and perhaps some information about functional groups present. So, in most cases, the 13C NMR is indeed less helpful than the 1H NMR.
The question then becomes, "why do people still take 13C NMRs?" Before going on, though, I should make it clear that people do not take 13C NMRs preferentially over the 1H, but rather in conjunction with it.
It primarily comes back to the fingerprint idea – when everybody tabulates 13C shifts of molecules they make, this gives chemist A the information they need to figure out whether they were successful in making what chemist B previously made. You might argue that the 1H is good enough as a fingerprint, but this is not always true, and anyway the consensus is that two is better than one: all major journals require submission of 13C NMR data for novel synthesised compounds.
The only other real case where the absolute 13C shifts are useful are when one needs to resolve very close peaks in 2D spectra (e.g. HSQC, HMBC), or in compounds with very few protons (thus rendering H–H or H–C correlations in 2D spectra less useful). Even then, it is not true to say that the 13C data is preferred over the 1H data.
All in all, your question is perfectly justified. In most cases, the 13C NMR is less useful as the 1H NMR, and only in some limited cases is it as useful as the 1H NMR.
In fact, there is a pretty recent perspective article by Liermann and Schlörer arguing that the 1D 13C NMR should not be recorded, except for in the special cases described in the previous paragraph. The authors also make the point that the 2D spectra serve as much more useful fingerprints and are also much better at validating a proposed structure for a molecule. Even though in crowded spectra the 13C fingerprint may be more useful than the 1H fingerprint, it's still less useful than the 2D data, where peaks are dispersed in two dimensions.
- Liermann, J. C.; Schlörer, N. E. Data handling in NMR facilities and assignment of NMR spectra in synthetic chemistry labs: Why electronic structure validation should become part of the routine. Magn. Reson. Chem. 2017, 1–7. DOI: 10.1002/mrc.4675.