That $5bn is a sunk cost, and Arianespace should be, within reason, able to deliver as many of them as ESA wants. My point is that it's not clear that ESA actually has a huge problem here; an Ariane 6 launch would appear to cost them similar to or less than a Falcon 9 launch does NASA (never mind a Falcon 9 Heavy, for which NASA pays about 200 million a shot; the bigger Ariane 6 variant sits somewhere between the two in role). This is a change from Ariane 5, which really was far more expensive (almost twice the cost).
It's just totally nonsensical to talk about price when Falcon 9 has no competition on price. SpaceX is rationally going to charge the highest price customers will pay. If a launch costs them $20m but no one else can do comparable kg-to-orbit priced lower than $80m (at much lower volume of launches), they will charge $70-80m.
should be, within reason, able to deliver as many of them as ESA wants
Where "within reason" means 1-2% of launches Falcon 9 can do. Again, if Ariane 6 internal costs were $20m and they could do 150 launches/year, you would see actual competition and prices going down, and Jevons paradox with a lot of new launch demand.
As a _launch customer_, it doesn't _really_ matter to ESA what the underlying cost is, only what they are _charged_. For the time being, Ariane 6 isn't drastically more expensive than the list price for the competition, and is, as above, _cheaper than the cost that other space agencies are actually paying for Falcon 9_.
If ESA was actually a commercial launch company, this would be different, but they're not. (Arianespace _is_, kind of, and _it_ should be far more concerned about this).
For practical purposes the number of Ariane 6 launches is gated by demand. Over the long term you'd probably expect it to be 5 to 10 per year, same as Ariane 5 used to be.
> For the time being, Ariane 6 isn't drastically more expensive than the list price for the competition
That's because SpaceX is soaking up its spare capacity with Starlink. I expect once that market is saturated SpaceX's launch prices will begin plummeting, as it seeks to maximise volume through market share.
More critically: SpaceX discounts for volume contracts. And it's the only launch company offering the kind of cadence populating a LEO constellation requires.
> "My point is that it's not clear that ESA actually has a huge problem here"
It's not about the ESA as a client and those bespoke science payloads; it's about (mass-produced) European satellite constellations, and similar high-volume, low-cost payloads.