You ask a very loaded question that has a lot of different answers.
These answers could take books to fully explain, and you'll run into many different opinions on why things are the way they are, and exactly how they should be different, but I'll try to answer them from a few different angles.
First, the proximate answer to your basic question of why it takes so long to go from Austin, TX, to Los Angeles, is because you start out on the Texas Eagle, which travels to San Antonio and has scheduled recovery time of an hour or so (to account for delays en route from Chicago, which can be unpredictable due to the variability of freight traffic), followed by a five-hour layover in San Antonio where through cars from the Texas Eagle are attached to the back of the Sunset Limited, that is coming from New Orleans. This, right off the bat, adds six hours to your scheduled trip.
Next, due to the same variable freight traffic (and single-track nature of the railroad, though that is being addressed over time as Union Pacific invests in double-tracking the route), the Sunset Limited has up to four hours of recovery time between San Antonio and Los Angeles. So, that makes for a combined total of 10 extra hours vs. moving continuously on a journey from Austin to Los Angeles.
Your next question is "why can't there be more funding to fix this?" Well, if you've watched the news regarding budget debates, I think you have your answer right there. If your question was more on the philosophical level of "why are we allowing ourselves as a nation to be in this position with respect to infrastructure and funding priorities," well, there's another book or two right there.
The question of speed limits on the railroad is the result of various federal regulations regarding track design and maintenance standards, as well as equipment requirements. Nationally, there is a maximum speed limit of 79 mph for any railroad not equipped with some sort of automatic train stop system (the actual rule is that speeds of 80 mph or above require this system, hence you can go up to 79 and not have it). Nowadays, the systems have to be even more advanced, with issues such as grade crossing timing and various other things coming into play. The cost of doing so is enormous, hence why it hasn't already been done in too many places by now.
The issue of express trains is a bit different. The simple economic reality is that there is very little justification for express trains except in time-sensitive corridors where there is lots of other service to pick up the local stops. The time you save by running your hypothetical Chicago-St. Louis-Little Rock-Dallas-Austin-El Paso-Tucson-Los Angeles train, even at upgraded (90-100 mph) speeds would be relatively little vs. the significant revenue you'd lose by skipping so many intermediate markets. Basically, someone who is in a hurry to get from Tucson to Los Angeles won't be taking the train, so you're not going to get more Tucson-Los Angeles riders by skipping the intermediate stops and offering a (for example) 7 hour trip, when they could fly it in an hour and a half. Meanwhile, the money you lose by not stopping at Maricopa (and, in an ideal world, that would be Phoenix instead), Yuma and Palm Springs, for example, would far outweigh whatever you might gain by skipping a few intermediate stops (and, for smaller stops, the time penalty for stopping is somewhere along the lines of 3-6 minutes per stop; depending on track speed through the area and also ridership at that stop).
Having more passenger trains that aren't on freight routes is a great ideal goal, but is not a practical option except in some of the denser corridors. Long-distance trains between the midwest and west coast will basically never have an entirely passenger-only right of way. There are too many vast empty expanses in between to justify running the frequent service that would justify dedicated right of way. Even if the right of way was free, track construction and maintenance would be too expensive for too little service. We face that right now on the Southwest Chief route (which is a more direct Chicago-Los Angeles train), where track through Colorado and New Mexico currently has no freight traffic. The host railroad, BNSF, wants to abandon that route, forcing the Chief to move to a more southerly route via northern Texas and Oklahoma, unless someone comes up with (I can't remember the exact figure, but I think it's something along the lines of) tens of millions of dollars per year to keep the line intact. And that's not even talking faster-than-79 mph service. There may be a reprieve for the route, if the states involved come up with the extra money (or lobby their congressiona delegation to find the money somewhere), but clearly it's hard on a grand scale to justify that kind of financial investment for such a small amount of service.
The bigger answer is that decades ago, we as a society and nation decided (consciously or not) that we were going to tilt the economics of transportation by putting metric-s***-tons of money into highways (and aviation), and essentially nothing into railroads. The results weren't surprising. Railroads (particularly passenger rail) struggled, and automobile travel became ingrained in the public mindset as a sort of default. In order to attempt to correct it, passenger rail has been attacked as being "subsidized" and representative of "government waste" by many, making it even more difficult to correct the imbalance in our transportation network.