It may not be that they can't, but that it's just not worth the effort to do it. They don't get anything for it, and it isn't even a game that is played competitively (or much at all) very much any more. Let's face it, it is a tough record to beat and would take some time and effort. Not worth it when the reward is minimal.
Actually in a sense he was paid to set it because he set it as a result of getting paid for doing what he was doing at the time. Brunswick paid him for years to do exhibitions/challenge matches, and often he would continue his run after he won if he was on a good run. On top of that it was THE game at the time so he also had incentive to hold the record in it because it meant something. On top of that he stood to gain financially. He might pick up more sponsors, and it certainly made it more likely that Brunswick would keep him on the payroll longer and maybe even increase his salary etc.
Today's players have none of those incentives, but even so if you paid Schmidt or Hohmann or any other of several players to travel around for years doing straight pool exhibition matches on the same equipment and they would continue any good high runs after winning then you still might see them break it even without those incentives Mosconi had. You may want to argue this, but what cannot be argued is that Mosconi had way more opportunity and incentive to break the record than any player of today.
I personally think if there was a real incentive to break the record today you would see it broken quickly. And I'm not talking a million dollars either. I'm talking enough to make it worth the effort. Let's say a person or company put up $30,000 for anyone who could break the record (meaning more than one person would win that amount if more than one person could do it) on the same equipment within a year. The players were made aware of the offer and they knew for sure that the person or entity making it was reputable and legitimate and they would actually receive the payment if they did it. The other stipulation is that the entire run must be filmed at all times from at least two camera angles, and if one camera has to be stopped to change the memory card or for any other reason the other camera has to remain filming continuously during that time. Meaning that while balls are being hit, both cameras have to be running. If one camera has to be turned off, no balls can be hit during that time and the other camera still has to continue filming and then when the second camera is back filming the player can resume his run.
Not only do I think the record would be broken, it would be broken by more than one person, and probably by more than one within two months. Why hasn't someone or some company with a lot of cash put up an offer like this? A) because they don't want to lose their money, and B) because a lot of people would be mad at them for enabling the breaking of a record many people wanted Mosconi to hold for all of time, and to be fair, C) because they don't stand a lot to gain from it except for maybe a company like cuetec who could make the offer only to their sponsored players so when the record was broken they could market the fact that they record was broken with a cuetec.