The vast majority of passenger will use HEx or Crossrail as part of a longer journey. How much of an inconvenience is that additional time going to be for long distance airline passengers, or those using HS2?
Depends - if you are going Heathrow to Gloucester, or Heathrow to Stafford or having some other hourly onward connection, those minutes might save a whole hour off your journey!
You also have to deal with factors like "would you rather spend 8 or 9 minutes on a train, or waiting at an airport/station with its facilities like shops, cafes, restaurants designed to make waiting more pleasurable?".
The superior frequency of Crossrail
Undoubtedly superior from T4 (4 vs 0), slightly superior from Central (6 vs 4), significantly inferior from T5 (4 vs 2).
And if a HEx is just after a Liz at Central, then people might wait because they'd be at Old Oak / Paddington faster. That depends on how much the premium is, and how much time they save. Certainly they do it for Mets that get overtaken by Chilterns.
Let's say the 10tph (4+4+2) at Central going to London fit into a 5 minute headway pattern:
00: HEx
05: Liz from T4
10: Liz from T5
15: Hex
20: Liz from T4
25: blank
and repeat for 30 to 55
Then from 10-15, 20-30, 40-45 and 50-00, HEx is the next train. That's 30 minutes of each hour - half the time!
Let's flip it round then:
00: Liz from T4
05: HEx
10: Liz from T5
15: Liz from T4
20: Hex
25: blank
and repeat for 30 to 55
That's still 20 minutes (4 lots of 5 minutes) when HEx is next. And HEx would overtake the Lizzies from T4, which might mean people wait for the HEx.
And let's look at T5:
- the first pattern, maximising 'HEx-is-next' at Central puts the Liz 10 minutes behind the HEx, getting 20 minutes where it's the next train (but the HEx will overtake the Liz, so will always get you to OOC/Paddington fastest - which would be a selling point that will get people on HEx)
- the second pattern, minimising 'HEx-is-next' at Central puts the Liz 5 minutes behind the HEx, getting just 10 minutes an hour when it's the next train.
Assuming you mean the price will drop in response to competition from Crossrail, won't this just make the service less economic to run?
Not at all - it makes it more economical. Basic supply and demand!
Let's say continuing with a £20 fare means they get 10 passengers per train as most people decide that the £10 premium is too high a price - that's £200/train in revenue.
But if they lowered it to £12 - a premium of about £2 vs TfL - they might be able to persuade 150 passengers to board each train. Because £2 could very well be worth the quicker time to OOC/Paddington vs TfL. That's £1800/train in revenue.
HEx is running the trains whatever, but demand is much lowered due to the competition, so it needs to maximise revenue per train. The marginal costs per passenger are low, so it has two ways to go - rely on a handful of total idiots paying £100 each (perhaps because it is £100), or getting the masses on by not charging that much more than TfL.