Having worked with IP lawyers on multiple consumer electronic products across multiple companies, I believe you are over-simplifying the situation. Every IP lawyer I've talked to didn't care about tivoization -- if you want to go run your own code on our hardware, great, good luck. The main issue with GPLv3 was always the patent clause: http://www.gnu.org/licenses/gpl-3.0.en.html#section11
I've never met an IP lawyer working for a company with many (hundreds to thousands) of patents allow use of the GPLv3, out of fear that it could undermine their ability to enforce patent rights defensively. Hardware companies produce a ton of patents. The manufacturers of routers, cars, and even Apple care deeply about their patents. They're not willing to toy with some untested clause in a license of some free software, when there is a perfectly usable version of that software without such a clause.
IANAL so I don't know for sure if this is the case, but speaking from experience, this is what lawyers have always told me.
Second, companies generally don't make it easy for users to run custom software on their products for a few reasons. You generally put software on products one of two ways: physically, or over-the-air (wifi/ethernet/some other way). With both methods, "signed" payloads are usually used for one of two reasons: to make sure it is error free. It's difficult to have the device already know the checksum, but calculating a signature against a pre-installed signing certificate is easy and works pretty well. You also get the added benefit of decreasing the surface area for remote attackers, since only the trusted company can sign the payloads. Typically, also, physical writing is "disabled" during assembly (e.g. not populating components, sealing off access, etc.) which helps keep costs down and keep the design looking slick.
The second reason "signed" payloads are used is for "Tivoization". I've never heard anyone say "we don't want customers putting their own software on a device they purchased." No doubt it happens, but it is rare for sure.
Should companies spend more time and resources to make it easy for their customers to modify their devices, in a sane and secure manner? Possibly. But in today's cutthroat consumer-electronics world, you'd be hard pressed to find a company willing to spend that extra engineering effort on something so frivolous.