It would be vastly easier for businesses which wish to let their employees out early enough to enjoy the sunlight to change their hours for a few months than for the entirety of society to change their sense of time.
Also, you'd be surprised how many clocks are not Internet-connected, as a lot of people still rely on clocks on their microwave, oven, car radio, etc. And in my case, I am absolutely reliant on one (or, often, like three) completely dumb alarm clocks, because they aren't subject to the whims of my phone doing dumb things like not ringing when it should.
Actually it wouldn't, because businesses have their hours set based upon the entirety of society's sense of time.
If you are scheduling a meeting, you will specify the time by the clock, but how to decide what time, can be decided by whatever else is applicable, such as when it is light or dark outside, or other considerations, and then know what time on the clock that time will be, to schedule.
Yes, many clock won't and shouldn't need to be Internet. Even so, you can also to use a sundial or pocketwatch, anyways. I also use "dumb" alarm clocks, actually.