It only support 32k parts in total (or in reality that means in practice 16k parts of source and 16k parts of parity).

Lets take 100GB of data (relatively large, but within realm of reason of what someone might want to protect), that means each part will be ~6MB in size. But you're thinking you also created 100GB of parity data (6MB*16384 parity parts) so you're well protected. You're wrong.

Now lets say one has 20000 random bit error over that 100GB. Not a lot of errors, but guess what, par will not be able to protect you (assuming those 20000 errors are spread over > 16384 blocks it precalculated in the source). so at the simplest level , 20KB of errors can be unrecoverable.

par2 was created for usenet when a) the size of binaries being posted wasn't so large b) the size of article parts being posted wasn't so large c) the error model they were trying to protect was whole articles not coming through or equivalently having errors. In the olden days of usenet binary posting you would see many "part repost requests", that basically disappeared with par (then quickly par2) introduction. It fails badly with many other error models.