I don't see anything wrong in the way Tony does it. The flat fee is for labour, parts extra . Sometimes it'll be £84 (or whatever) for something small, other times it'll take 3 visits. He's taking the risk of a troublesome, time-heavy fix away from the customer.
I don't do it that way because I don't see the need. I find people accept that some jobs cost more than others. I also charge "HRPC" prices for parts. I've got a fair bit of cash tied up in parts, so I don't have to go off to get them and return another day. So I charge for that.
I don't generally find that people have looked up a part on the internet, and if they do, as soon as they realise it'll take a couple of days to come they don't mind paying for convenience.
If I haven't got the part and have to go miles to get it, that's difficult sometimes. There's always what someone on a forum like this call "white bulls*it" - you can say something like yes, you're going to charge for going off to get the part it looks like you'll need, but you won't be charging if it's the wrong part. They have the choice of getting the part themselves, (but by implication, it may be wrong, and you'll have to come another time...)
The phrase "as much as I can get away with" sounds nasty. "As much as the market will stand and keep me busy" is realistic, surely, and amounts to something similar?
I daresay we could debate the moralities of pricing until the dogs come home. I charge for how long a job would take me do do again, if I've just done it for the first time and it's taken ages, but that's a personal choice.
If you're changing a pump and the valves work, it's 15 minutes, but if they need changing and the system won't refill, it's hours. So if you quote £200 and it takes 20 minutes, what then?
Suppose you replace a part where the mfrs retail price is say £150, but you know you can use the same thing without their badge on it which costs say £30 (WE know what that mght be..). Do you charge £150, or £30, or something in between?
Travel's another bone to chew - people accept that going into London is extra, but if you don't happen to be in their town, tough! If I have to travel more than about 20 minutes each way, ie 7-8 miles, the price goes up, whether they know it or not.
Sometimes I charge very little, if a job's small and local - can pay dividends in goodwill and future work.