If the rest of the car is in good shape, throwing another engine into it wouldn't be the end of the world. It is a service item after all, with a finite lifespan. If people like their car enough, it's certainly an option, and inevitable if you keep it long enough.
The problem with direct injection is it burns a lot more of the fuel compared to port injection, thereby you get a lot more carbon in the exhaust. Look at the tailpipe tips! I've seen some badly tuned TFSIs with soot covering the back of the car too.
A lot of that carbon gets into the oil via blow by, which forms sludge, so the mechanic was technically correct. As these engines age, the only way to keep them clean internally is to change the oil frequently because as the rings / cylinders wear out, the blow by gets worse, compounding the problem.
Drop the sump, clean/replace the pick up pipe carry on. But get it done asap because every time you see that stop light, bearings are momentarily running dry.
