Beware of quoted figures of starting tractive effort: for several decades it was conventional to give this, for diesels, as one quarter of the total weight (on powered axles) of the locomotive. A reasonable rule of thumb, perhaps, since (before the great improvements in anti-wheel-slip electronic controls starting in the late 1970s) this was about the adhesion limit: try to exert more tractive force than about a quarter of the weight on drivers and you'd just spin your wheels uselessly. But it is at best an approximation.
After that disclaimer… In answer to your question, with a high starting tractive effort you can get a train started, but how fast you can keep it moving depends on the tractive effort you can continue to exert after starting. Since starting tractive effort is greater than continuous t.e., this will be a lower figure. For the locomotives you mention, minimum continuous speed is, I guess, somewhere between 10 and 15 m.p.h. Below this speed, using full engine power will result in a tractive effort greater than the continuous tractive effort: a locomotive can do this for a while, but the traction motors will heat up, ultimately to a damaging (as in: I smell smoke!) temperature. So, to run at a speed lower than the continuous speed for a lengthy period, you have to run the engine at less than full power.
So the advantage of higher continuous tractive effort is that you can make free use of the full engine power at a low but still useful speed.
For switching, the restriction to low speed isn't that important. So one alternative to getting an MP-15 in the 1970s would have been to take an old RS-3 and replace the Alco engine with an EMD 12-567 from a scrapped passenger unit: STARTING tractive effort is limited by adhesion, so this hybrid (call it an "RS-3M") could start as heavy a train as an MP-15 or an Alco roadswitcher with the original, more powerful, engine. With only 1200 horsepower, you're not going to go very fast, but the continuous speed is probably now below 10 m.p.h. So you can do heavy switching all day, or run a branch-line freight on lousy track where the safe speed is very VERY low. Penn Central and its successor Conrail converted over a hundred RS-3 in this way.