If you read the abacus chapter you'll see that the trackdisk in 1.2 doesn't use the word sync to find where the track starts, it reads more than a track worth and then uses the cpu to search through the result. I think they might have stopped doing that in release.
This is correct, and indeed, they stopped this nonsense in kickstart 2.0. The reason for this "feature" in 1.3 was likely because there is a mis-documentation in the RKRMs Hardware book on how the sync-word feature works. According to the RKRMs, the sync word works by PAULA watching the incoming MFM stream and enabling DMA as soon as the pattern is detected. However, this is incorrect, PAULA does more than that. If the sync word is enabled, and DMA is running, PAULA *also* resynchronizes on every detected sync word. This makes an important difference in the track gap, where synchronization can be lost, and it is not clear that the start of the track aligns correctly to the end of it, bit-wise. From the RKRM description, you would have only gotten unaligned MFM data in the buffer after the track gap, and hence would need to re-align manually - which is what they did. However, PAULA is not that stupid. Whenever it sees the sync word, it restarts at a word-boundary from that sync-word on, discharging any incomplete or unsynchronized bits.
The disk format wasn't optimal for the hardware either. For reading it would make more sense if there was just one $4489 per track, this wouldn't affect writing as you have to write an entire track even if you have only modified one byte anyway. It looks like they wanted to allow sector writing because paula can search for the sync word when writing, but it doesn't have any way of checking which sector it would be writing to. My guess is the disk format was decided on and code hacked to work on the hardware that existed but nobody had time, or thought it would be a good idea, to go back and review the design after the hardware was finished.
Actually, no. If you only had a single sync word, then PAULA had only a single chance of finding the sync word per track, i.e. in worst case, an entire track would have to be read twice: First, to detect the sync word - if you enabled PAULA right after the sync word is passing under the head - and second to get the full data. With the sector layout, the MFM reader will at most spoil an entire sector plus the track gap, which is a much smaller part of the track.
Some games, however, use the entire track to store data, with a minimal track gap, and thus squeeze more bytes into a track. Of course at the expense of possibly reading tracks slower by missing the sync word in the first rotation.
The PC floppy disk controller uses the reverse: It synchronizes on every sector, has a much larger inter-sector gap, and does no buffering, i.e. sectors are read and written individually. With the relatively short sector gap the Amiga trackdisk layout has, this would be rather impossible. The chance of overwriting the next sector would be very high. For the PCs, the uncertainty in write alignment is compensated with the higher inter-sector gap (i.e. the sector can overflow a little bit behind its natural location, then fills the sector gap without overwriting the next sector header).