I would expect ULA to hang around a while longer. If for no other reason than "assured access to space" or redundancy in launch vehicles. Regardless of how over-priced ULA may or may not be. Unless another launch vehicle service provider pops up to provide the US Government with certified rockets. The US Government is not going to be comfortable with only Falcon 9 rockets. They need a Delta, Atlas, or any other certified rocket to back stop Spacex. Foreign rockets are out of the question. Blue Origin? Maybe, but not for a while yet. Until then, I don't see ULA going away. They still have a backlog to get through. Satellite operators are loath to rely on a single launch provider (although they do have access to foreign rockets), so they will keep spreading the business around.
On the other hand: would the US government accept "assured access to space" redundancy with actual reusable rockets. Meaning because rockets are no longer being expended in the near future, would a previously flown booster provide "redundancy" in case another Falcon 9 mission fails? I think not, because there are lots of other related issues revolving around a failed mission (possible damage to launch pads, failure in the expendable upper stage, etc.). But I do think it deserves a closer look in light of what the competition (ULA) would charge being an only 40% provider (minimum # of launches in order to remain viable). For example: if a reusable Falcon 9 mission only costs $10 million, but it cost $100 million for the same mission from ULA. Would the need for different suppliers justify the outrageous price difference? Perhaps of fleet of used Falcon 9 boosters sitting in the hanger, with multiple launch pads available would provide the needed redundancy in access to space. I just see the whole launcher redundancy becoming obsolete in the face of reusable boosters... maybe.
At the very least, if the pricing is $10M vs. $100M (I realize we're making up numbers to illustrate orders of magnitude), every $100M launch the US government pays for is going to get all kinds of negative publicity. Meanwhile, with reusability and order of magnitude lower pricing, SpaceX is going to be opening up space to a large number of new entrants. If SpaceX is also flying weekly (sounds crazy today, but that might be a holiday week in a few years), the "assured access to space" thing is going to be a lot less important.
And the usual reason for a second supplier - for pricing power as you pit them against each other - isn't going to sound too good in the media when you can get 10+ flights with one provider for the cost of 1 flight from the "keep them honest" supplier
Heck - that's such a huge reduction in cost that relative to today's pricing, all the satellites you want to build just got better than free.
It just throws everything about space flight that we think we know today up in the air. Wouldn't it be amusing if this marked the start of real space tourism - not going up close to the boundary for a few minutes, but going all the way into orbit for a week of vacation, and then returning?
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One thought I have about how things might change - once reusability starts happening for real, I see a change coming in rocket design. As I understand things today, rockets are designed around being the bare minimum weight and structure strength necessary to accomplish the mission. Every gram of anything past that point is waste.
When you stop throwing away $60M launch vehicles routinely, maybe it makes more sense to build heavier rockets with more structural integrity that can handle the stresses of multiple launches. Even if that cost goes up to $80M for the rocket and $500k for the propellant each launch, you're saving crazy amounts of money on the second launch and every launch afterwards.
Heck - maybe SpaceX puts payloads on a bigger Falcon Heavy in the future strictly because the 3 first stages can be recovered (yes - I am presuming that SpaceX figures out how to actually make that happen, instead of just the artists rendering of how it might work), where a Falcon with 1 first stage would be at it's limit and couldn't carry the fuel to be recovered.