What you described isn't what's considered a rat bike... it's just a dirty rough nasty bike that's ridden a lot. Rat bikes have intentional things done that aren't normal in the type of bike you describe. Much of what is done is contrived, especially the aging process for portions of it. Few rat bikes are truly just aged, virtually everyone I've seen has had stuff done to accentuate the rattiness.
I've done a lot of reading on rat rods mostly because I'm looking at a specific type of painting I want to use. It seems there's a bit of a divide there much like I see with another sort of bike. Some are pointing out there are two different types of rods, the weird stuff done with rat rods and the more normal but not show finished street rods, often called hot rods. One is an exaggeration of everything, the other looks more like the original hot rods of the 40s and 50s often in primer. I see this with bikes. The rat bikes exaggerate some things, like having jockey shifters with weird handles or levers, distressed look parts that are made that way, off the wall stuff is quite common and much of the work isn't really functionally sensible. There is even intentional rusting like the rat rods do. Wild enough, there is now a trend with some rat rod guys to use fiberglass bodies (steel ones aren't that common in the 30s models) drill/hacking "rust holes" in them and paint along with surface preps that imitates surface rust and rusted edges.
Much like the cars, many rat bikes are built somewhat dysfunctional. Unusual bend bars with cramped or stretched ergonomics. Those with fat oversize front tires work against handling, as do the 2" travel shortened front and hard tail or short travel rear ends are far from the hot trick for ridability. They're sort of an anti-establishment statement of the builder/rider.
I will also point out there are places for all, but the hot rod bikes. These are the type of bikes like the original superbikes and similar modified but not quite fitting other categories of bikes. They aren't ratted out, they may just be a bit rough around the edges and are "frequent fliers" - aka they're ridden regularly. A production version was the old Nighthawk S and the early GPz550/750/1100 and ELR. This could also include some of the milder customizing of standard bikes, but not including customs or cruisers of any sort. They have their niche. They're also not quite clubman or cafe bikes either, just reworked standards and some early customs modified to become more standard in layout. I've often spoken of the "hot rod" bikes like those old Superbikes were and the in-line/vert twin/etc bikes of the early 70s with maybe superbike bars, a set of pipes, a semi or non stock paint job, and custom seat. They have no place in the areas except vintage and not all are. The hot rod bikes don't lose function for aesthetics, they just are modified and almost always "in process".
That's kind of been the case with my SR500, but now it fits the street/tracker niche. My Zephyr falls in the hot rod bike zone I speak of, not being sport with the fairing and clip ons and old enough in design and style to fall outside the current standard/naked bike definitions. It also described the factory look of the Nighthawk S with the unusual bodywork, which is almost not quite matching up, but works with the graphics.
I know it's breaking things down to niches, but I like that for the most part. Not that it's to divide riders, just to be able to describe what one is doing.
Of course those niches get blurred a bit depending on perceptions. Some people see street/trackers as bikes with fat tires where I see them as exactly what they started as... guys took flat trackers and put them on the street. I had several friends do that before the term street/tracker ever existed, back in 1975. One even went from being built as a flat tracker with street equipment to actually being put on a flat track competitively, because it had both a Champion frame and flat track suspension and a built engine. Now it seems someone lowers forks, sticks on fat tires and may even lower the suspension and call it a street/tracker. Frequently those in the grey zone are more brat/bobber/rat niches than tracker, but whatever...