This is actually a really interesting question. On a spherical earth with tectonic motion, subduction is necessary. That is, in some places like the Mid-Atlantic ridge, spreading occurs, and in places like the trench off the western coast of South America, subduction occurs and the old land slides under itself, and the whole process is in perpetual repetition. However, when one looks at one of many graphical representations of the relative ages of the earth at the sea floor, there isn't any evidence of subduction.
In this image (and many others like it), red represents "younger" land, and blue the oldest. In these images, I see evidence that the continents are older than everything else, and the only thing happening as far as tectonics is expansion. On a spherical earth, unless the sphere itself is growing, this can't happen. In an infinite plane, it's not entirely out of the question to think that the plane is ever-expanding, particularly when one notes that the overwhelming majority of this expansion appears in the southern hemidisc. Cover the lower half of this image with a hand, then the upper, and compare the amount of area that is red. Also, near the center of the disc (the north pole) the continents are still largely crunched together. Farther south near the ice rim, land masses are greatly fractured and spread widely apart.
Now, of course, this isn't my data so I take it with a grain of salt, but given that simply doing an image search for "sea floor age" (that's how I got this one) returns many, many different images all showing the same relative ages, then I consider them worth a little more salt. It isn't evidence in the empirical sense, but it's certainly compelling. I think geologists simply assume that subduction must happen because an earth that is a fixed sphere demands it, but it's not happening.
Actually, this is proof that subduction
is happening. As the plates slide underneath each other at the trenches in a process called flux-melting, magma is created and forms volcano arcs that run parallel to the subduction trenches (unless you can explain other reasons for the formation of magma/volcanoes running parallel to trenches according to Flat Earth Theory).
If you look at the map you posted, it clearly shows the oldest part of the crust is the farthest away from the known magma eruptions along the sea-floor (such as the Mid-Atlantic Ridge) as the crust is spread out along the diverging plates which then sink underneath the continental plates.
Now because continental crust is thicker and less dense than oceanic crust, it is the oceanic that sinks below the continental forcing the movement of the continents, not the growth of them. On the continental crust where the plates converge they'll form mountains rather than sinking below one another. And as this kind of movement continues, the continents will all be pushed back together as the crust continuously replaces itself rather than expanding.
And you skipped my question of how we can map the interior of the round Earth with seismic waves.