If you plot a P-V diagram of a Carnot cycle, you will see that the work output is very low relative to other cycles, resulting in low MEP.

What do you mean by "Maximum Mean effective pressure"? MEP is resulted from the cycle actual work output divided by the displacement volume. High MEP means you have generated more work with a smaller volume displacement.

As you said, MEP for a piston-engine is just swept-volume-specific work. There is a maximum BMEP value achievable over the cycle and it's relatively low compared to other ideal cycles (e.g., Miller cycle). High MEP for a cycle does not necessarily equate with the highest achievable cycle efficiency. In practicle vehicle applications, however, there are some efficiency advantages to high BMEP - e.g., reduced powerplant size and mass can reduce vehicle road load. Some engne designs with broad operational areas of high BMEP also allow part-load operation with fairly low pumping and frictional losses (boosted SIDI engines, for example).