On the contrary
It could be done.
Construct a solar powered, ion-driven microsatellite weighing, say, 10kg. Then build, say, 269 more of them. With that sort of number being built they'd be fairly cheap. You'd have 5x Delta heavy-lift rocket launches (450kg payload capacity), one every 6 months for 3 years. Get them out of earth orbit. Expensive- probably a billion or two- but not un-doable.
Each one should contain sensors to determine threats to human life- particulate radiation, solar wind, intense EM issues, anything that goes wonky in the Van Allen belt, that sort of thing.
You've then got a load of data from a huge range of points all along the route to Mars- and at different times. You can see all sorts of seasonal variations and trends.
Then use the other $78Bn to build a vessel that can survive in the conditions highlighted by your little sensor microsats. It just needs to be able to launch once- doesn't need to re-enter the atmosphere. Hell, take it up in bits. Again, you're talking huge numbers of rockets being built, so the processes for their manufacture can be streamlined.
So you're talking about a vehicle that doesn't need to go through our atmosphere, doesn't need to go through the Martian atmosphere and could probably be nuclear powered-VASIMR propelled. That's not going to be an overly expensive vehicle.
You then need an excursion module and that's probably not too much of a problem; mars has quite a thin atmosphere and lower gravity. Plus with all the extra space on the mothership not dedicated to landing you could fit a whole load of sensors and find somewhere safe, strong and flat to land.
You also have the payoff of making space launches much, much cheaper as you're churning out heavy-lift rockets. Which makes NASA all the more relevant as more people can afford to do "space" stuff. So they'd get funding for a second mission no problem.