As far as the issue of taking sick days: I don't often get sick enough to stay home. The worst thing I get 90% of the time is a minor cold, enough to be annoying but not to prevent me from working. I will typically go in and share this with my coworkers
. If I have something slightly worse, I will "work from home" which is more or less standard practice in my industry and what all my coworkers do when they are sick. And if I am sick enough that I don't feel I can work effectively, I will take a sick day. I take on average, less than one sick day a year. It is not a big deal at my current work place to take a sick day - we don't even have a set balance of sick time, it's just "take it if you need it." So generally I feel this policy encourages me to work at home as much as I feel up to, which I think is good.
As far as sick time vs. PTO vs. whatever. I personally am a fan of PTO. Obviously for someone like me who doesn't take much sick time, it allows me to get more vacation time. However! I am also against it, because some people view "PTO" as "vacation" and thus do not take days off when they are sick (either sharing their germs, or pretending to work at home but not really working.) PTO is worse for those who get sick more often and better for those who get sick less often, obviously, and I think small companies like it because it hedges their bets a bit. But I think, like the airline baggage check fee, while it makes sense on the surface, it incentivizes bad behavior.
The flip side is, some people view "sick time" as "PTO", as days off they are entitled to. I know someone who worked someplace where they could roll over sick time. She worked there for years, and when she got burned out and was planning on quitting, she took an average of two "mental health days" every week for like 6 months. I also know of a place that offered up to 25 sick days - but they had to change the policy because some people seemed to be taking those 25 days every year because they felt entitled to them.