Work should be done so stations are off the main line.
You want to rebuild every station?
And people thought HS2 was expensive!
Look, yes. If you have mixed traffic, then having passing platforms/loops is a very sensible idea. And in the US, where you have acres of space then maybe you can achieve this. But (for the most part) not in dense UK towns.
And here's the thing, Switches & Crossings are expensive and maintenance-intensive. If you are building a branch line (or a metro), where you can reasonably expect every train to stop at every station, then obviously that's fine - no work required. If youre building a new ICE line, then you design in passing loops. But putting a load of S&C at every station imposes a perpetual maintenance cost that - in the proper analysis - starts to favour just building a separate express line that runs through the countryside and leaves the old lines for local services.
The problem is with the plea of "can't we make the existing tracks better?" or "why do we have to build a new HS line? Wouldn't it be cheaper to build new local rail?".
The existing lines already go through towns and cities. So it makes sense to dedicate them to local/regional services. Trying to make them express-ish (as we have) and then building a new "local" line would involve carving a new corridor through the town. Or slapping the "local" station on the edge of town - not very useful.
Existing urban stations also tend to be hemmed in by other development. If it's a simple 2-track/2-platform, then building in passing loops usually involves demolishing both platforms, installing the new tracks where the platform used to be and putting new platforms further out. i.e. you're totally rebuilding the station.
I've seen some sensible suggestions from people on schedule modifications that often include trains on a route not stopping at every station during busy times. If a train is full, unless there is a request to stop, bypassing stations can increase average speeds.
This is not a sensible suggestion. If your idea is to have request stops in order to raise average speeds and therefore play nicer with non-stop express trains... you're setting yourself up for a highly unreliable service. What if every stop is requested (at busy times, it will be!)? You have to serve every stop or else people won't trust it for the purpose of getting to work. And if every stop is requested, your express trains are going to end up being delayed behind the local service.
There's no sense otherwise to stop if there isn't the space to take on more passengers.
If that's the case, you need to be prioritising more local services at the expense of ICE services, or running longer trains and extending the platform. If you are leaving passengers standing on a platform and making them late for work, then they'll revert to driving - even if they can't really afford it.
existing infrastructure can used more efficiently.
The most efficient way of using infrastructure in terms of trains-per-hour and passengers-per-hour is for every train to run to the same service pattern and stop at every station. This is how metros run at 90-second headways and shift 30k PPH in each direction using one line in each direction.
Once past ~150mph, the costs start going vertical to go faster.
Not really. Above 225mph maintenance load starts running up, but 200 is a perfectly well-established baseline for modern (high speed) inter-city passenger rail. The ITE define "high speed rail" as ~120mph on existing infra, and >160mph on new-build. 150mph is table stakes. But yes, trying to torture >150mph out of an old alignment is always going to be difficult and expensive.
In the case of London <> Scotland, there's already services. One can take a plane if in a hurry, take to the rails to make a journey of it and even travel overnight a bit slower but without losing waking hours making the trip.
1. The airports are full, so the proposal is to build a third runway at Heathrow. This massively increases noise and air pollution and we should be trying to move away from short-haul aviation entirely. Better to build a new long-distance line (which will be 200mph because it's 2025, not 1825 - this is a solved problem thanks to France, Japan and Alan Wickens).
2. It's not about the speed. It's about having the dedicated line which isn't wiggling through towns and villages you have no intention of stopping in. If you're building a new ICE line, it'll be 200mph. But that's not the point. The dedicated line is the point.
3. Nonetheless, in getting to 200mph, you adequately replace short-haul aviation within ~800miles. Furthermore, you increase the distance you can travel in a given time - for instance, HS2 will probably get attached to HS1 some time after 2050 and international services will be possible. A Manchester or Glasgow to Paris service benefits substantially from doing 200mph on a dedicated line vs 120mph on a legacy line (sometimes, but with TSRs down to 80mph in wiggly or urban areas, old tunnels, etc).
4. SLEEPERS. Yes! So, you're thinking small. You're thinking London-Scotland sleepers, which we've done for 100+ years. But at some point we'll have international services. If we had 200mph across Europe (pull your finger out Germany), then Paris to BUDAPEST could be an overnight sleeper. Hell, if you had HSR across the US you could do NYC-LA in <15hours! HSR predominantly helps your national ICE services in daytime (or regional in US) - it gets the Texas triangle within 75minutes of each other, and the midwest is all within 120mins. But stitch those HSR networks together and you suddenly get a really profound sleeper option. Nobody is thinking about high speed sleepers and how that can compete with mid-haul aviation.
Sleepers are already having a renaissance in Europe (Nightjet, etc). 200mph could pretty much cover the continent overnight. We don't need to stretch to 250-300+mph. The well-understood 200mph is basically "good enough".
The money for HSR could be spent elsewhere to improve or even just clean up infrastructure that hasn't been seen to for decades.
Where? Specifically. Actionable.
Okay, so I've said the point is the new line. Let's say we built HS2 as a 120-150mph ballasted track - do it cheap and slowish. We've got a new line, we've got traffic segregation. Great. Just how much do you honestly think we're going to save? The money is in the land, the civils, the legals. Whether you align and build a brand new track for 150 or 200mph is a marginal saving, especially in the UK with high land prices. And this is the sad thing. Nobody - nobody - who has said "let's spend the money on improving the existing network" has any actual actionable proposal for how you would treble capacity on the existing network through upgrades. Nor how they would avoid the HELL of the West Coast Route Modernisation (3x over budget, under-delivered, almost a decade of weekend closures and cancellations - the precise reason they said "yeah, we'll build a new relief line - we're not making that mistake again on the MML or ECML"). There's a few nostalgists who claim the Great Central line should be reopened (it's been built over, and doesn't go to Birmingham). They're also obsessed with the Woodhead Line and tunnels, even though moving the high-voltage Grid lines would cost £1Bn to start with.