60% isn't exactly the greatest confidence booster -- that's almost at the level of a coin flip.
That's actually not quite so.
So, for example, let’s imagine a vaccine with a proven efficacy of 80%. This means that – out of the people in the clinical trial – those who received the vaccine were at a 80% lower risk of developing disease than the group who received the placebo. This is calculated by comparing the number of cases of disease in the vaccinated group versus the placebo group. An efficacy of 80% does not mean that 20% of the vaccinated group will become ill.
VE is calculated as (ARU - ARV) / ARU. If the ARU is say 0.7, i.e. without a vaccine you get ill 70% "of the time" (more correctly 70% of the population would--something like this was estimated early in the pandemic) then a VE of 0.6 means that that ARV is just 0.28, i.e. only a bit more than a quarter of the vaccinated would get infected. And that's much better than a coin flip. So ARV, which is really what you want to compare with the coin flip, really depends both on the ARU and VE.
Also, the VE numbers you're talking about concern hospitalization... and the ARU for that is pretty far from a coin flip to begin with--something like 5% (based on an IHR of 7% among the infected, and assuming 70% of the pop gets infected). So, in this latter case, comparing two numbers (ARU, ARV) that are far from a coin flip... with a coin flip is not exactly insightful. ARV would be 0.02 in this case, i.e. your "hospitalization chance" drops from 5% to 2% when vaccinated, under these assumptions. That
may not look like much (absolute) difference for individual protection, but it does mean needing less than half as many hospital beds etc.
Somewhat o/t, but in a 3rd world country (that can't afford mRNA vaccines) even the J&J vaccine could make quite a difference as anyone needing hospital care and not getting it at all is fairly likely to die; see what shortages of oxygen have caused in such counties.
And hospitalization isn't the only thing worth considering. Deaths were not considered in that CDC
study you're quoting from, but the J&J vaccine seems to do better in that regard:
in early August, a clinical trial that followed nearly 500,000 health care workers in South Africa found that the J&J vaccine was 71% effective against hospitalization and 95% effective against death due to the delta variant.
I'm not going to comment on how the CDC chooses to phrase their findings when comparing vaccines, but I'll just add that efficiency at single point in time is not the whole story.