This is because the DFT is circular. In the transmitter we modulate by treating data mapped to a complex constellation (such as QAM) as a single bin in the DFT, we can then group many of these bins together to effectively create a massive amount of narrowband modulations all in parallel. We would use the inverse DFT in the transmitter to create the result we would expect to have in the time domain, no different if we did actually did modulate multiple adjacent channels in parallel using classical time domain modulation approaches.
This results in one block of time domain data which is all fine and good until we transmit this block over a wireless channel with multipath delay. At the receiver we will get multiple copies with delays consistent with the "delay spread" of the channel. If we transmit multiple blocks one after the other, the delayed copies of each block will smear into the next ones, causing distortion that we can't easily resolve with the intended receiver implementation that uses FFT's to restore the constellations and finally the data. So a time buffer is needed between the blocks being transmitted to allow for the delayed copies to settle before the next block starts.
Now comes to rescue the consideration of the circular nature of the DFT: If we take the data that is at the end of a block of data and attach it to the beginning (and we will use the minimum amount of time allowed by the worst case delay spread expected), and then use that in the transmitter, then when we take the FFT of the actual block of data in the receiver, the beginning of the block will properly have the delayed copies of the same constellations that were at the end of the block. With that it is then feasible to completely correct / resolve the delayed copies and remove the distortion effects due to multipath.
The delay being less than a symbol duration does not mean there would be no distortion due to multipath, it just means we can get away with a simple "one-tap equalizer" for each constellation (simple gain / phase adjust) due to flat fading in each subchannel, given that we can have a complete copy of the delay components for the symbol.
For further details, please refer to these posts:
OFDM. Cyclic Prefix and ISI