Actually, as a car-free resident of LA for close to a decade (grad school then work), I'd say LA's public transit system is pretty good, and the major obstacles to making it better are rampant NIMBYism and the Bus Riders' Union (aka the Bus Drivers' Union). The bus system is a well though-out grid (though you do often need to use buses from multiple agencies for historical reasons), with both local and express service on heavily used routes. There are extensive connections between bus and rail service, and connections between rail lines are also generally well-timed, so there isn't much waiting on the platform. There's also a contactless payment system (TAP) that works on almost all transit agencies in LA County.
Frankly, the at-grade Red Line system wouldn't fare any better than buses in today's LA traffic.
LACMTA has been expaning rail and "bus rapid transit" (Orange and Silver lines), but is hamstrung by neighborhood groups who bring frivolous lawsuits that only make the rail service less useful and more expensive. Some recent examples:
1) Residents near Dorsey High School sued LACMTA to stop the Expo Line (some social justice nonsense about how rail transit is for the 1%), which resulted only in millions of extra taxpayer costs and Expo Line trains having to stop before crossing Farmdale Ave (adding several minutes to every trip).
2) Beverly Hills has an enormous traffic problem on Wilshire Blvd., but has tried to stop all of the following: a freeway; signal priority for buses on Wilshire; bus lanes on Wilshire; and a subway extension under Wilshire (some law-and-order nonsense about how rail transit is for the 99%).
3) South San Fernando Valley residents wanted a subway instead of surface rail on what is now the Orange Line, and they lobbied the state legislature to make it illegal to build a surface rail line on the right of way... so they got Bus Rapid Transit, which uses extra-long buses. The infrastructure cost is about half that of rail, but the operating costs are three times as high (because the line is at capacity, and each bus holds 1/3rd as many passengers as a train).
Land acquisition is actually an insignificant cost in building LA rail transit lines because LACMTA already purchased the rights of way they need years ago for peanuts. The Expo Line and Orange Line rights of way were purchased directly from railroads that didn't want them anymore. The proposed Crenshaw Corridor and Gold Line Foothill Extension would mostly use old Southern Pacific rights of way (that LACMTA already owns).
Tunneling is expensive in any city, but how else are you going to fix traffic? There isn't room to expand surface streets, and if you thought it was difficult and expensive to get a light rail or subway built... whoa boy, you don't want to even think about a new freeway.
As for the airport connection: There's already a free shuttle from the Green Line (Aviation Station, I believe) that loops through all the terminals, just like the parking lot shuttles. LACMTA also runs "Flyaway" tour-style buses from LAX and Burbank to a bunch of places around the city, where they connect with other transit lines. The reason the train doesn't stop in the terminals is that the LA airport authority has been saying (for the last 30 years) that they're going to demolish and rebuild the terminals in a year or two.