I don't have any scientifically based surveys, however, I have anecdotal evidence from audits performed in nearly 100 departments throughout the USA and Canada. In reviewing those audits, it is much easier to cite examples of those two or three agencies that were NOT currently out of space or soon to be out of space. 

In addition to performing audits, I have taught over 750 property and evidence management classes to over 30,000 individuals from all 50 states, and all of the Providences in Canada. I routinely perform an informal poll in these classes and ask how many agencies represented think they have a space problem. There is an overwhelming response, probably in the 90th percentile, from personnel that believe their agency has a space problem. As a result, I strongly agree with your premise that there is a nationwide problem with overcrowded property/evidence rooms. 

The simple reason for the overcrowded property and evidence rooms in most agencies is that they don't assign sufficient man-hours to the purging process. Performing the research needed for purging is a very labor-intensive process. Each item of evidence has a measure of time associated with its removal. Once a property officer gets behind in purging, he/she cannot get caught up without spending additional hours or shortcutting the process. 

When a property officer doesn't purge as many items as he/she takes in, the agency will eventually run out of space. It is common for agencies to remove only two or three items for every 10 items coming in. 

At this rate, the inventory can easily double in 3 or 4 years. Few departments get rid of as many items every year as they receive. However, it can be done with sufficient personnel and support from the top of the organization. 

Regarding online auctions, www.propertyroom.com has a positive reputation among over 3,000 law enforcement agencies that now use this service. There may be some agencies that conduct their own auctions using www.ebay.com or their own in-house websites, but the actual labor costs to maintain the website and conduct the auction probably exceeds the revenue.  A quote from Joe, "we generally don't have space problems, we have system problem in purging the no longer needed evidence."  It's not unusual for inventories to be comprised of 70% - 80% misdemeanor evidence. In most states the SOL - Statute of Limitation is one year, some states are longer. The question to always, ask unless the case has a warrant or appeal has been filed, why do we have all of the misdemeanor evidence? Easy answer, insufficient time or staffing and processes to routinely evaluate aged evidence.