Yes, changing c would definitely lead to stuff like "reality does not exist as we know it".
c goes into many other constants and determines most of the laws, especially in e&m. Realistically, atoms would not be able to hold up against the pressure to collapse, pretty much all matter (if it still existed) would condense to very very very cold solids instantly. We'd be shut out of most light from the sun for potentially hundreds of thousands of years.
I'm just starting my big graduate theoretical physics journey so i really can't do all the relativistic quantum math yet, take what i say with a grain of salt!
AAUI the basic laws can be expressed with dimensionless constants, and in modern physics c is a conversion factor for convenience. I don't know if there's a way to adjust all of the "real" physical constants conjointly which would amount to "just like the Standard Model with a different c".
I want to say it's not incoherent to say e.g. "Newtonian mechanics, but relativistic, with a different c", except of course e.g. Newtonian gravity with its action at a distance doesn't fit, and I wonder if really even contact forces fully work if you try to follow through every detail.
c goes into many other constants and determines most of the laws, especially in e&m. Realistically, atoms would not be able to hold up against the pressure to collapse, pretty much all matter (if it still existed) would condense to very very very cold solids instantly. We'd be shut out of most light from the sun for potentially hundreds of thousands of years.
I'm just starting my big graduate theoretical physics journey so i really can't do all the relativistic quantum math yet, take what i say with a grain of salt!