Just wait for Spectrum. The install fee, if there is any, will cover all of this. And they primarily use contractors who are paid by piece work, so their incentive is to install your lines and equipment as fast as possible so they can do as many installs per day as they can squeeze in to maximize their pay. They will do it the fastest and easiest way possible, which is counter to what you want.

Call Spectrum back and ask for an in house installer and not a contractor. They will probably still send a contractor first anyways, who will have a magnetic sign on their truck/van/beat up Honda Civic that says Authorized Installer for Spectrum. Unless that tech is willing to install it to the level and method you are comfortable with you have every right to send them away and request an in house installer. The only wrinkle is if a new line has to be brought in from the street and it's buried and not aerial, Spectrum will send another specialist contractor out to do what is known as a make ready, and they will run a new buried cable to your house if that is what is needed, but a make ready will stop there and hand it off to an inside installer.

If the flipper cut out all of the coax it's probably because former installers ran it through the floor, punched it through walls, etc. I have seen some wild stuff in my travels. This is your home, so make sure you are happy with the end result.

When we bought our house it was a nightmare of that crap and I gutted it ALL during our initial renovation so I could patch it and do it properly. I happen to be a former electrician and wanted both coax add ethernet ran all over the housr so I just got the materials and pulled in everything together, brought it all back to a closet where my network equipment is installed so the coax junction wasn't outside, and then ran a new feed cable from there to where the aerial drop hits my house. But Spectrum had to come in and terminate and connect everything when we were done.

If you want the inside wiring to be done very specifically then you are better off either running that yourself or hiring an electrician or low voltage contractor to run it. But everything outside from the street or pole up to your house, known as the demarc (point of demarcation between what Spectrum owns and you own) or MPOE (minimum point of entry) is owned and must be maintained and installed by Spectrum.