Good eyesight is important for flying.
It's important, but really, not as important as you think.
I have poor eyesight and I fly all the time. I have -5 in one eye and -5.5 in the other, plus an astigmatism. I don't know how well corrected it is, but I pass the eye tests, so that must mean it is at least 20/40. The last time I had an eye test, I nearly failed for near vision, and the AME suggested I look into bifocals. I found that strange as I have never had any issue seeing the instruments while flying and wearing my regular glasses which are calibrated for distant vision.
You wouldnt want your pilot to see the runway wrong or fly into a flag pole.
These are not things that are what a pilot with poor eyesight worries about. If you are near a flag pole, you have already made some serious mistakes. Pilots do worry about hitting radio towers, guy wires, etc, and honestly, often those are invisible even with good eyesight. They are best avoided with maps.
Poor eyesight makes the chance of a mid-air collision more likely, particularly if you are operating VFR (that is, not flying an airliner). Flying and airliner you are IFR all the time, and the vast majority of the time you are also flying in airspace where ATC is separating all the aircraft. (Climbing out of a Class B airport, you pass through class E airspace before entering Class A airspace, and in the E space, there can be VFRs that you need to look for.) Point is: not really all that much eyeballing going on.
So despite the law every airline has their own restrictions and i remember talking to veteran pilots as airline companies downsize and hire from time to time so they often steal pilots from each other instead of going for new ones. If an airline accepts you for being a pilot they usually cover your training fees (but they will take a cut off your salary till its paid).
Practice varies by country. I can only speak to the US.
Regarding vision requirements, I could not find anything on the web to imply that airlines have vision requirements separate and apart from the FAA. The airlines require you possess a valid Class I medical, and that has a vision component, but I'm not sure there's more than that. I'm honestly curious, so would love a pointer to move information.
Regarding training, I do not believe there are any US carriers that will take you ab initio, but that is more common in some other countries. For example, United Airlines requires you to have 1000 hours turbine time and an ATP rating to be hired. (
https://www.united.com/web/en-US/content/company/career/pilot.aspx) I'm sure they'll train you in their aircraft and procedures, but any pilot with an ATP is already highly trained. Most of these pilots are moving up from smaller carriers where they built time in smaller aircraft (making smaller money). Those carriers, in turn, like to see a commercial rating and a few hundred hours multi engine to start a minimum. The pilots usually pay their own way to get that far, and you can also consider the time working for minor ducats at a regional carrier as a kind of pilot cost, too.
Pilots are paid well simply because you have to handle peoples lives and strict rules are in place because of this. A disgruntled pilot could be a danger to others.
Pilots, generally, are not paid well until they are captains with high seniority flying for major airlines. Here is a bit about that:
https://www.pea.com/airline-pilot-salary/ Starting pilots working for regional airlines make something in the $20k's. Median for all airline pilots of ~$100k which isn't bad, but this includes the older pilots. I suspect STRONGLY that your pilots today are never going to be making the money that high-seniority pilots today make.
As it happens, lots of people have jobs where they could be a danger to many others, and a lot of those jobs don't pay either.
I remember an article about flying saying that flying is actually safer than driving because of the number of accidents vs the number of flights and plane crashes and that so much more technology has gone into airplane safety compared to cars as airplanes can cost millions and airlines will still buy them whereas cars cost thousands and people wont buy if they cost more (except for luxury).
Flying on an airline is supremely safe. Statistically, it is probably safer than standing in your kitchen or bathroom. There are kinds of flying that are not nearly as safe, but most people will not be exposed to them. I am a private pilot, and fly piston singles. The statistics are hard to correlate, since driving accident rates are usually calculated per mile and flying per hour, etc, but overall, I'd say operating VFR in good weather is a bit safer than driving, and operating IFR in IMC is somewhat less safe than driving.