When you have a profit to defend, you tend to do your best. Any government funding they've received have been in the form of bonds or tax breaks. If you define those as making a company "public" vs "private", you've about identified every business in the country in some form or another.
Outside of federal/state regulators, Brightline doesn't answer to taxpayers. They answer to shareholders.
I can't think of one thing that the government does better or more efficiently than the public sector - especially in transportation.
Most stations have been paid for by local governments. Miami Dade really wanted Aventura for example. Also a slight correction, BL is private equity, so has bond holders and ownership stakes, not public stock. Aside from the rather large tax-free aspect of the bonds, it seems clear the state gave BL a clear road to leasing rights of way, etc. BL Florida also took small federal grants for railroad safety. When financing became tougher, and Softbank (Japan) deteriorated, two things happened: BL explored partnerships with public commuter/transit rail in South Florida and Orlando; and Softbank sold BL to Mubadala (with US management). I say all this as a BL supporter, more or less! Florida's governor back in the early 2000's was far from the only one to reject Amtrak funding. Even Chris Christie in NJ said Gateway entailed too much obligation - while diverting the money to similarly obligated highways. The question in Florida though has always been who is profiting through land deals or bonds. And the commuter/transit partnerships are a benefit to the public as well as perhaps necessary for growth, given the private need to find money outside the most obvious ridership demands.
You would think Tri-rail covered the territory from Miami to West Palm, but just as I-95 is paralleled by the Turnpike, there's a higher level of service for those who pay more, and just as there are gated communities everywhere, and as in Central Florida homeowner associations controlling most middle class housing. The literal fence between affluence and poverty at the Fort Lauderdale BL (secured by magnetometers) and public bus depot and adjacent distressed sidewalk campers is stark, but hardly felt on the BL side. In other words it's a typical fast-growing area in demographics, but very sunny and brash, and somewhat less forgiving. Constrained by the Everglades (contested though) and the ocean, it's an intensive very long suburban-urban mix.
I don't know if Amtrak or its host railroads would have allowed all the drone video coverage by Roaming Railfan, a very nice level of transparency for the foamers in us. The publicity, such as time-lapse animations, for projects like the Portal Bridge in NJ barely exists. For highway projects, it varies. The Philadelphia highway collapse reconstruction was well publicized, as is the new tunnel between Hampton and Norfolk in Virginia.
Of course basing a railroad around real estate development goes back to the origin of the FEC in South Florida, and, briefly, the Keys. Although Key West had already been the largest settlement in South Florida, when Miami was just a campsite and a few farms. Julia Tuttle in Miami sent her orange blossoms to Henry Flagler during a freeze, the Brickells developed the other side of the river, and an alcohol-free community full of learning and edifying concerts came about, with drinking only allowed in Flagler's hotel. But credit also goes to the Bahamian workers of an earlier generation. In a sense, nothing has changed.
One bit of news out of South Florida, a new aggressive state law is overriding local control of protected areas for more intensive housing, with the Clevelander art deco hotel on Miami Beach likely to face the wrecking ball. For a decade it has been fueling the all-night party scene, barely controlled by public police forces, and now will reap the benefits of demolition. A bizarre version of the transit-oriented development law in California overriding localities. It's not just the U.S. - Irish politics is roiled with housing issues.
Brightline should be seen as healthy competition, not a cudgel against public funding. The frequency is great, for example.