When you're developing a physical theory, you're free to define your quantities as you like. You won't get away with $s = d + t$ since dimensions of addends don't match, but you can still come up with a whole bunch of equations, e.g. $s = d × t$.

In the end, physical theories are useful insofar they can describe the real world and predict what happens. Speed (or velocity) defined as $s = d / t$ is very useful for this: objects having the same velocity share a lot of interesting properties, like having a constant distance between them, or going from start to finish in an equal amount of time. Speed defined as $s = d × t$ just doesn't predict anything useful, that's why nobody defines it like this.

When you're developing a physical theory, you're free to define your quantities as you like. You won't get away with $s = d + t$ since dimensions of addends don't match, but you can still come up with a whole bunch of equations, e.g. $s = d × t$.

In the end, physical theories are useful insofar they can describe the real world and predict what happens. Speed (or velocity) defined as $s = d / t$ is very useful for this: objects having the same velocity share a lot of interesting properties, like having a constant distance between them, or going from start to finish in an equal amount of time. Speed defined as $s = d × t$ just doesn't predict anything useful (or very little), that's why nobody defines it like this.