Amazing how hard it can be to have a productive discussion, when definitions keep changing!
"Flat rate" is simply telling the customer "I will do the job for $X." This is essentially what Mr.Sparky does - with the addition of a service charge to go look at the job. No free estimates there.
Just where does that 'flat rate' price come from? Invariably, there is some reference to your past experience, and allowance for whatever complicating factors there might be. Given a large enough sample base, you can fairly state that a certain task will take "H" hours, use "$P" in materials, require the use of certain equipment (surcharge there), and come up with "$X" as your price.
The advantage to various software and franchise operations is that they allow you to draw upon a larger sample size, and have a support system to help keep material costs up to date.
T&M is an arrangement akin to a blank check; that's something you won't trust to just anyone. It has its' uses - especially when an established contractor has a project of unknown scope and duration.
For example, painting the Golden Gate bridge is an instance where T&M can work well - that job never ends! By contrast, painting your house ought to lend itself to 'flat rate' pricing.
Another key to the Mr. Sparky approach is to have the guy doing the estimate arrive in a fully stocked truck, ready to do the job RIGHT NOW. There is pressure- if nothing else, that service call fee- to get the customer to commit right now to having the work done. Such immediate service can allow you to charge a premium.
