It would be possible to preserve the concept of a code of points but assign the points in different ways that would avoid these problems, and no doubt encourage different ones.
That is true.1. A skater can win the competition in the short program, robbing the long program of any interest or purpose.
It is also true that a skater can win from 4th or 6th or 7th place without worrying about what order the other skaters she beats finish the long program in -- if she beats the short program leader in the long program by more than the leader beat her in the short, then she wins.
The fact that former tends to happen more often than the latter indicates that the balance between points available in the short and points available in the long is not currently calibrated to make the long program worth more. I think the main reason because although there are more opportunities to make mistakes in the long program, there are also more opportunities to make up for them with other skills.
If TPTB agreed that long programs should be more do-or-die, then it would be possible within the existing general framework to change the balance of elements between short and long programs and to change the severity of the penalties for failed elements in the long.
This is primarily true for the elite senior men, under the current scale of values, because triple axels and quads still earn significant points even when failed. When successful, they earn even more points, easily mitigating any points lost to mistakes on elements that started out with lower values to begin with.2 The risk-reward ratio is out of balance. Risk-reward ought to go like this. If you take a big risk and it is successful, you win. If you take a big risk and you fail, you lose. You should not be able to take big risks, fail repeatedly, and win anyway.
This was less true ca. 2010 and before, and it remains less true in other disciplines and at lower levels.
Again, it would be possible -- although difficult in practice the way judges are currently assigned and trained -- to rewrite the criteria for Performance/Execution, Choreography, and Interpretation to disregard the quality of the skating and/or to penalize visible flaws more explicitly.3. The three performance components should not be tied so firmly to skating skills. If a skater exhibits fine blade work, deep edges, excellent speed, and busy feet, then that skater deserves strong SS and TR scores. If that same performance is marred by many flaws, then that skater's artistic components should tank appropriately.
Personally, I think there is plenty of room within the existing general framework for improvement in the way the criteria for these components are written and the ways judges are trained to score them.
But I would be surprised if the ISU decided to rewrite the criteria for these components so thoroughly that actual skating skill would be completely irrelevant to these components, since they are after all part of a skating contest, not an interpretation-through-movement contest that just happens to take place on an ice surface with blades on the feet.
I also think that even if the rules were rewritten to explicitly encourage judges to penalize visible errors that interfere with appreciation of the performance, that would end up including some kinds of technical weaknesses that judges find disruptive but most viewers don't pay attention to in addition to those that fans tend to dwell on long after the skater and the judges' minds have moved on.
E.g., if a skater is breaking forward at the waist with each stroke and scratching on the toepicks while skating backward, the effect may be so much like nails on a chalkboard to the judges that they would penalize heavily under PE even without falls and stumbles. Whereas nonskaters might be more bothered by a fall or two in an otherwise well-skated program and, if watching on video, might not hear the scratching at all.
I.e., I do think it would be an improvement to explicitly encourage judges to reflect errors in these components. But I don't think that people whose prime interest is to evaluate skating and people whose prime interest is to enjoy error-free programs will always have a meeting of the minds on how much it is appropriate for a skater's artistic components to tank.