How will the BE-4 engine "Save taxpayer money"?

Question

In this explanation of the Blue Origin BE-4 engine, the text says:

LOWEST COST

Blue Origin’s BE-4 requires NO taxpayer dollars.

Fully funded

The BE-4 is fully paid for by the private sector requiring no government funding for development. A recent NASA “Justification for Other Than Full and Open Competition” for buying additional Space Shuttle Main Engines states that a traditional engine development program will cost more than $2.2 billion.

Save taxpayer money

The BE-4 saves taxpayers an additional $3 billion in national security launch costs over 20 years by providing higher thrust – 1.1 million pounds versus 860,000 pounds for the RD-180 – which enables a greater payload capability and allows for the removal of a solid rocket motor at more than 10 million per flight for comparable missions.

Do I understand this correctly - the BE-4 engine will save US taxpayers $3 billion over 20 years because it has 28% more thrust than RD-180 engine? The math is 300 launches times 10 million per launch = 3 billion? Or 150 launches times 20 million (two boosters) per launch?

It sort-of sounds like private investment is considered "free money" and they'll never want to recover their investment by charging more. That's often a criticism of companies using government money for development - that it's "not fair" because it's "free money". But I don't usually follow these arguments very closely so maybe I am missing some subtleties.

However there does seem to be a much more extensive discussion of the issues related to the RD-180 and BE-4 engines and US government satellite launches in the 2014 The Space Review article ULA, Blue Origin and the BE-4 engine. Here is a snippet, but there is much more to read in the full article:

The companies issued statements to try to dispel the perceived purpose of the Blue Origin BE-4 engine: “The BE-4 is not a direct replacement for the RD-180 that powers ULA’s Atlas V rocket, however two BE-4s are expected to provide the engine thrust for the next generation ULA vehicles. The details related to ULA’s next generation vehicles—which will maintain the key heritage components of ULA’s Atlas and Delta rockets that provide world class mission assurance and reliability—will be announced at a later date.”

However, ULA posted this on its Twitter account: “We intend to use a pair of BE-4s on the base Atlas with even better performance.” In addition, the handout for the BE-4 states the engine will be built for “…meeting both commercial requirements and those of the U.S. Air Forces’s Evolved Expendable Launch Vehicle (EELV) program.”

Answer 1

The 'national security launch costs' refer to launches on Atlas V. The current version uses the Russian RD-180 engine. A few years ago, continued availability of this engine became questionable, and the US government started pushing for a replacement.

One candidate for developing this replacement engine was Aerojet Rocketdyne:

In June 2014, Aerojet Rocketdyne proposed that the US Federal government "fund an all-new, U.S.-sourced rocket propulsion system", the 2,200-kilonewton-class (500,000 lbf) thrust kerosene/LOX AR-1 rocket engine. As of June 2014, Aerojet's early projection was that the cost of the each engine would be under US$25 million per pair of engines—not including the up to US\$1 billion estimated development cost to be funded by the US Government. Aerojet believed that the AR-1 could replace the RD-180 in the US Evolved Expendable Launch Vehicle fleet, and that it would be more affordable.[7]

Blue Origin, in contrast, says it'll develop the engine using its own funds, and (presumably*) recoup its investment by selling engines, adding a few million to the per-engine cost.

I'm saying "presumably" because Blue Origin can choose to not recoup its investment, and sell the engines at something closer to the marginal manufacturing cost.

The AR-1 is designed as a drop-in replacement for the RD-180 and can be used on the current Atlas V. The BE-4 cannot be used on the Atlas V, but will be used on the Vulcan.

The \$3 billion in additional savings is a more difficult claim to verify. There doesn't seem to be any documentation for it other than the BO website.

In the 2000-2009 timeframe, there were 17 military launches on Atlas V, in 2010-2019 I count 43 including GPS satellites, so 300 launches in 20 years sounds plausible. So the savings of \$10M/mission by removing one booster could account for the entire \$3B.