This sort of thing absolutely happens; useful search terms are "sex ratio distortion", "segregation distortion" (i.e. modifying the ratios with which different chromosomes segregate), and "meiotic drive" (a specific form of segregation distortion).
Your scenario (Y-chromosome genes forcing all offspring to be male) is much less common than the reverse (X-chromosome genes, or other genomic elements, forcing all offspring to be female), because it's easy for an all-female lineage to maintain itself by parthenogenesis. Lyttle (1991) says:
Strong Y drive is of necessity transitory, since drive
suppression must either evolve very quickly or the population will be pushed
to extinction. This may explain why few Y drive systems have been observed
However, Lyttle goes on to describe
- W-chromosome drive in butterflies (in butterflies, females are the heterogametic sex — the sex chromosomes are Z and W, ZZ individuals are male and ZW individuals are female). So this is a little bit like your Y-chromosome example, except that the populations end up all-female rather than all-male
- male drive in mosquitoes
Jaenike (2001) says
Although several species exhibit Y drive, X drive is far more common.
Table 1 in that paper lists Y-drive examples in houseflies, mosquitoes, medflies, lemmings, and field mice. (I would include an image, but the table extends over 4 pages ...)
As for your final question,
I would therefore expect that such a mutation would spread, skewing the sex ratios away from 1:1 ... Have scenarios like the one I outlined above actually occurred in species? If not, why not?
I haven't dug through all the original literature that Jaenike (2001) cites, to see if there are populations in nature that are male-skewed due to selfish Y chromosomes. The point that Lyttle makes is that, even if you can find evidence of the existence of selfish Y chromosomes hiding in the population, it's very unlikely that these will persist in natural populations for very long, because of the strong selection against them at the population level (and from the rest of the genome); either the population will go extinct, or moderators will evolve that suppress the driving effect of the Y chromosome.
Jaenike, John. “Sex Chromosome Meiotic Drive.” Annual Review of Ecology and Systematics 32, no. 1 (2001): 25–49. https://doi.org/10.1146/annurev.ecolsys.32.081501.113958.
Lyttle, Terrence W. “Segregation Distorters.” Annual Review of Genetics 25, no. 1 (1991): 511–81. https://doi.org/10.1146/annurev.ge.25.120191.002455.