without seeing your situation, I won't put myself in the yea or nay camp.
skatona if you buy the remote pop up for kitchen sink drains, it comes with a tight elbow under the sink strainer so it sends your sink drain tailpiece horizontally instead of going down like we usually see it. This is a commercially sold and available product. Yes it is true that this horizontal pipe might get gunk in it, or that it will, and secondly that since it's prior to the P trap any smell the gunk would generate will come into your kitchen. BUT this is not the deal breaker kind of information that you were asking for. From that tight elbow, there is a slip joint to the tubular which goes over to your drain pipe (copper or PVC or whatever), and you have another slip joint at that connection. (((Anyway, that is what I have))). Any time I want to unscrew these slip joints I can do so, easily. I can look inside the tubular, and clean it out. I can look into the copper and clean it too. Easily for a few inches, not for three feet.
So, yes skatona you CAN "run your kitchen sink drain line through a few cabinets to get to the through-wall connection (due to layout of framing)." And the "rules" regarding where the p-trap needs to be will allow it, so that is a yes again. HOWEVER there are good reasons to encourage you to put the P trap closer to the sink drain than roughly 3 feet away. One is the reason described in this post already. Another one is that a P trap closer to the drain makes it easier to snake.
Where is your dishwasher connection? If it can be put close to the sink drain, then this will wash out the horizontal drain prior to the P trap, a lot.
The height from the floor is almost the same, of the pipe prior to the P trap and downstream of the P trap. So, there may be no NEED to put the P trap that far away. As a compromise, I'll suggest you put the P trap closer than 18" from the sink. The portion of pipe that follows the P trap is "Trap Arm" in the DWV code. It can be 2" diameter.