I think all the above answers are correct and inter-connected. Using PayPal only,
ebay has the control of money exchange and, at least theoretically,
ebay has the power to address grievances. Western Union aka BidPay and other wire services were used too often in a fraudulent manner without any recourse available on
ebay's part. The net result is a quasi-monopoly in which
ebay pulls the strings while at the same time removing a source(s) of competition and history of fraudulent transactions. I cannot speak for transactions outside the United States regarding PayPal's security, utility, and legality, but here in the US PayPal works very well and is my preference for payment. I have also had a few out-of-country PayPal payments with no problems, but these were for low-priced items.
The above said, one thing I've noticed about PayPal's use is that it is also the payment mode of preference by known fraudulent sellers; estatedoctor comes to mind. The onus is upon the buyer to demonstrate that the terms of the auction were not met (e.g., wrongful description, fake or counterfeit items, non-delivery of items). If the buyer is unable to provide this proof, the seller keeps the money and the buyer is out of luck. Further, the sum involved might not be worth the effort of filing a claim with PayPal. Both pamim003 and estatedoctor's negative and neutral feedbacks have a considerable number of complaints regarding non-delivery of items and no refund of the purchase price.
Further, PayPal gets a cut of every transaction in addition to
ebay's Final Value Fees. This goes back to the monopoly (quasi-monopoly in that there are other means for paying for an item, e.g., personal checks, money orders).
But with PayPal now carrying the ball, it's gonna have to more firmly enforce its own Terms of Payment and other rules.
ebay hasn't been addressing these grievances very well recently, at least in the Coins categories.