Quick answer is that it’s usually way more expensive to buy tickets just as you want them.
 
Say I want to buy a one-way ticket on EasyJet for London to Venice for tomorrow – it is 83 pounds if I buy it today. If I buy it today for September, it’s 31 pounds. So in this case, the difference is only about $100 USD, but often it’s $200 or $300 difference. In summer, particularly when there is high demand, the situation is worse.

Another thing to consider is that it may be tough even finding an open seat during summer.

For clarity, do you mean arrive to Europe with a one-way ticket only? Because that would present some problems.

 
That’s what I was getting at, yes.  I assume that would cause some logistical problems as there may be worries I would stay longer than the 90s allowed by my passport.

Without a visa allowing a longer stay, you can’t show up with a one-way ticket. You risk 1. denied check-in by the airline who share some responsibility and risk fines for not checking passengers for proper paperwork, 2. deportation unless you can cough up proof of onward travel, 3. fines for overstaying and bans from re-entry, 4. lots of hassles every time you try to travel in future with that passport—it will have a big + or X across the immigration stamp showing you were denied entry somewhere.

Better to choose your starting and return airports, and let everything inbetween be your fly-by-the-seat of your pants flexible-travel-experience. You can even choose to return from a different airport to save backtrack time and expense; this type of ticket is called “open jaw.” You could arrive to AMS and return from ATH, for example. They are often priced as half of each round trip as long as it’s same airline. Kayak and Mobissimo have good “multi-city” searches for this type of ticket.

Or, you could get the cheapest r/t to anywhere Europe, then use a low-cost airline to hop back a day or 2 before your scheduled return. www.whichbudget.com