infinite linear extension isn't logical or natural

Really ? If I double my speed, I travel twice as far in the same time. If I halve my speed, I travel half as far. Choose your multiples the relationship still stands. That's a linear relationship that can be extended infinitely, both logically and naturally.Once you get up to relativistic velocities, you may have a hard time continuing to double your speed, and the elapsed time depends on whose watch you're consulting.

More seriously - linear relationships are often simplified models that are only useful within a restricted domain. Galileo's various weights all hit the ground at the same time, but a feather would take a lot longer.