Medicare is a great program and is actually very efficient when compared to private insurance. However yes, there is far too much fraud, waste and abuse. Problem is where one group sees such things, others see a food on the table. There are times when the federal government has sought to shut down those who abuse or have committed fraud against Medicare, only to have a judge reinstate because the government did not have the "right to deprive ... of income".
For Medicare to truly run effectively and less expensively, it would have to take pages from how many Europeans run such programs. That however would entail far more stringent price controls, service restrictions and so forth than one assumes most Americans would tolerate.
Think about it; you don't need several hospitals all within one geographic area all accepting Medicare, but with various census rates and outcomes. Simply choose the one that meets standards of performance and so forth and send everyone there; that however would probably effectively put the rest out of business. Same with pharmacies, suppliers and so forth with equal results for the others.
What the federal government could and should do is establish one agency to oversee/set prices/create a formulary for *ALL* federal government health care spending. Everything from medications to supplies and so forth. For something as simple and basic as say Tylenol prices vary depending upon which federal agency is doing the purchasing. VA, Medicare, military, federal government employee health and retiree programs, etc.. all have different rates. Just think what would happen to prices if the federal government used it's vast purchasing power as a whole for healthcare, instead of piecemeal.
This is one reason why healthcare is so much cheaper say in EU countries. The government negotiates prices it will pay for everything from aspirin to replacement joints.