Hi Hans,
I don't think that an MP3 recording function is a "must have" (on any keyboard). When you are recording directly to MP3 format you cannot restore the original, uncompressed sound quality. So I would record always in wav format first. In a second step, you can convert the wav file(s) into MP3 format (on the computer) very quickly. Converting is also possible in batch mode, if needed.
The ability to play MP3 files, on the other hand, would be desirable for the SX600 in my opinion. But this is not really a problem either, because storage space (on USB sticks, hard drives or SSDs) is currently cheaper than ever before. A stereo wav file requires 10 MB per minute and an MP3 file (at a usable bit rate of 192 kbps and upwards) around 3 MB per minute. Given the size of the USB sticks available today, in my opinion it is no problem to save everything in wav format. I don't think that's a major problem, since the MP3s are usually first on the computer anyway. So you can also quickly convert your existing MP3 files into wav format to can play it on the SX600.
P.S.
For me, the lack of a touch display is the knockout criterion for the SX600. For this very reason, I would never buy an SX600. I also can't understand why Yamaha used the S670 case for the SX600 as well. So I generally recommend at least an SX700.
Best regards,
Chris