It is arguably the opposite of corruption. Everyone is treated the same and everything is checked in order. The option to pay for a faster approval would be corruption. This is just government offices being chronically understaffed.

Well, the problem is that putting a price tag on government services makes them exclusionary to those who can't (or can barely) afford it while making no difference to those who easily can. It's like the old saying about fines: if you punish a crime with a fine, you only make it illegal for poor people.

That said, the processing time is probably more costly than the direct expenses because having to wait longer means you likely already pay a part of the mortage rate (most banks have start-up costs on these loans and you are generally expected to secure the loan before you have the approval). The entire process is expensive enough for the actual fees not to be a meaningful issue.