I just cut my second door for the auto door bottom this past weekend. I used a basic "skil saw" (Makita worm drive, but we all call them skilsaws, lol) and just made a whole lot of cuts and then broke off the remaining "fins" that were left (each was less than 1/8" wide), cleaned it up with a chisel then a sander. Fairly easy, but the results were not as good as the first door where I used a router. However, much less dust and mess. That is a LOT of material to cut away regardless of the tool used.
I originally intended to do a mortise in the center of the door so you couldn't see the door bottom at all, but that is a tricky cut to make even with a good router, a really long bit, and a steady hand. You can't set the door up and use gravity to assist, so you are cutting sideways any way you look at it. And the slightest tilt with a 1.5" bit sticking out will result in a pretty significantly uneven cut.
But bigger than the issue of making the cut without screwing it up or injuring myself, on interior doors you only have 1.5" total thickness, so when you cut out over an inch of thickness out, you have less than a half inch left. That is a bit janky on a particle board core door with an MDF veneer that makes up the first 1/8" of thickness. Even if the door is solid MDF and not particle board, 3/8" can break off (or split) pretty easily if you are trying to move the heavy door into place and drag a corner of the bottom. If the door was solid hardwood, that would be the only case where I would even consider doing a full mortise. But think about it, even with solid hardwood, a 1/4" thick, 1.5" long piece of wood sticking off the bottom of the door could break off pretty easily. Even after installation, catching a rug while closing it could rip a chunk off that door, and if it were 1/8" of MDF and 1/8" of particle board, the chances of breaking it off are almost a given. Not worth the effort IMHO.
So just insetting it on one side with a rabbet cut was better than mortising it inside the door, and since you can paint the aluminum door closer the same color as the door, it isn't really noticeable. In my case the door bottoms both face the space between the two doors, so even better.
The inner door on my theater is a 1 3/4" door, so I had much more material to support the door bottom. Plus it was just a flat slab with a hardwood veneer, which made it stronger than the MDF veneer of my outer door. I cut that one and didn't have to worry too much about snapping off a corner while installing the door.
The picture posted a few posts up is nearly identical to the cut I just made in the regular solid core interior door.
To answer your questions about the router, you can get longer bits, and a good plunge router will allow you to use the full length of the bit. You could even pull the bit out a little to get that extra reach, but while I might be OK making a 1.5" deep cut with a 1.25" deep bit, I would never try to do it with a 1" bit. As for width, you just adjust the guide and make several passes to get whatever width you want.
And don't forget, the door closer won't be the exact width of the door, you will have to cut it shorter, which you can do with a miter saw if you take it slow and have a regular carbide tipped blade. Take the inner parts out first and if you have to cut those too, pull the rubber parts out first and cut those by hand with a razor knife, and the aluminum channel piece with the miter saw. While a good 80 tooth blade will probably not catch the rubber seal and just cut through it, I wouldn't take the chance of it binding and yanking the whole piece out of my hands and mangling it (and maybe injuring me too).
I'm pretty sure I have some pics of my first door in my build thread, and I will be posting pics of the second door probably next weekend after it is fully installed.