No it isn't - I had one and it had a large widescreen navigation system, an electronic drive by wire accelerator, digital connection for all the gauges in the instrument cluster (Your temperature gauge isn't showing you the temperature, it's a representation of what the ECU has told it to display). It has fully digital oil level measurement, etc etc. The next 3 Series - from 2011-2019 - changed basically nothing and was more or less the same. There is almost no difference between a 2015 and a 2005 3 Series in terms of how many digital interior components there are. Neither car has a touch screen.
It is far from what you seem to think it is - all those things you think are manual and traditional are electronically controlled behind the scenes. It is a modern car in all respects.
You'd like a 2015 3 Series just as much as a 2005 if you like normal looking (Remember, it's the computer telling it what to display, there is no direct connection to whatever it is measuring) gauges and no touch screens.
I don't think these absolutely huge bills are quite as common as you seem to think. The reality is that you are not hugely likely to encounter a £5000 repair bill with a £15k 3 Series or a £2k 3 Series. You'll probably be fixing similar things - just more often with the cheaper car as it's twice the age, has twice the wear, etc etc. But at least the £15k car is much easier to find in good condition - I would be very surprised if any £2000 3 Series wasn't a pretty poor example.
Who is just as capable of working on the £15k 3 Series as well. Though he'd probably find himself doing so a bit less often.