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This comes up a lot on other websites where people talk about gap years and/or RTWs.

It's basically a case of doing what's best for you, as determined by some easy, but maybe a little time consuming, research. It's not hard to use the web to figure out air ticket prices from point A to point B. If you want to travel without premeditation, fine, but look at what prices are for tickets bought on short notice.

Depending on one's (ultimate) itinerary, it's possible to string together a bunch of flights on low-cost carriers (or even conventional airlines) that can be price-competitive with RTW tickets. On other itineraries, in particular when they involve travel to fairly remote places, or those served by only one airline (Easter Island is the poster boy for this) then the cost of a single one-way ticket can sometimes equal a big percentage of an RTW fare, with which that place would just be one of 16 destinations. But if your trip involves flying from one mega-hub to another mega-hub, then the RTW might not give you the most bang.

With the Oneworld RTW tickets, you can change dates without paying a fee, but changing the itinerary will require a $125 change fee (or its equivalent in other currencies.) So if you go crazy and keep re-issuing the ticket, it can add up. As for paper v. e-tickets, "open" segments on paper tickets still involve two fixed-in-cement cities; only the date is shown as "open." Date changes are free with both e- and paper tickets; route changes are charged in both.

On the other hand, the RTW ticket gives you two free checked bags, something you'll pay for (sometimes dearly) when flying on low-cost carriers, or using point-to-point fares. At $25 or $40 a pop, those bag costs can add up just as fast as re-issue charges. You'll also earn frequent flyer miles and benefits, something you might not be able to do flying budget airlines.

Read the rules, read the stickys, do some thought experiments, road test the online booking tool to see the final, real number (with taxes and airport fees) then duplicate the route using non-RTW flights, and see how it boils down.

I believe RTWs are one of the most flexible ways of traveling in premium classes for a reasonable amount of money.
If you really plan to change your routing several times mid drip this becomes costly and time consuming. I am using a lot of RTWs and usually have more then one open.
My strategy is: When i know the first part of a trip (say Asia to US) i book the ticket with the flights i want and the routing i need. The rest of the ticket is just for dummy flights and dummy dates. Then wen i need the ticket from US to Europe the next routing change and the third routing change for the last part of the trip.
I buy my tickets from a TA who knows what he is doing. Whenever i need changes i email him and he does everything for me. No need to spend time on the phone with airlines, wait at ticket counters. He charges a fee, but it is well worth it.
For that reason i also need electronic tickets, because then rerouting and ticket reissues are possible via email.

This strategy possibly does not make sense for somebody who is budget constrained on an economy ticket, because often there are cheaper ways in economy.
But traveling in F and repositioning one to one of the cheap starting points makes this a very flexible, convenient and inexpensive (for F) way of travel.

IT is also a good idea to compare RTW options with the other two alliances. *A and OW can be easily done online but ST is harder. The flexibilities and options for all three are different. I have done all three, and still find depending on my specific plans or lack of them one can be better than the others.

As several people state, planning is the key to happiness in RTW. Spontaneity is fine for dates, assuming there's availability, but routing should be defined as closely as possible prior to your departure. Thus...planning.

BTW, I have used them mostly for business travel when the RTW fare would be less than the F or C fare I would otherwise pay point to point. I would not think of an RTW economy option because it is usually cheaper another way AFAIK, but I have never bought a Y RTW.

Depending on how spontaneous you want to be you might also have difficulty finding availability at short notice.

I seem to recall posts on here complaining about lack of L availability on key routes. (making the assumption here that you are looking at an economy RTW ticket).