Sorry, don't want to be rude to TAs on this thread, but I would only use a TA if I were incompetent, unorganized, didn't know how to use the internet, or didn't have the time to plan my own trips.
I'd really like to have an answer - re: calling a TA to solve problems while on the trip - what problems require a TA? What problems require so much time that it sacrifices the travelers time? The only thing I can think of is if the TA messed up a trip detail & therefore, no seat on a plane, no room in the hotel?
Even for trips to many countries for the first time, I was able to gather everything we needed & so much more, & there were no holes in my planning. Travel message boards contain all the info anyone would need, plus many little know gems offered by actual travelers. I don't trust that a TA would have the time to be so thorough - it would not be cost effective.
We were in Europe when the volcano erupted in Iceland. We were scheduled to fly when all the airports, airlines, trains, & ferries were backed up and/or halted. I calmly made two quick calls & took care of everything, while everyone else on TV was panicking - 1 call to the hotel at our next stop to advise them we may be late, but to hold our room, & then one call to our current hotel's front desk to put a room on hold in case we needed to stay. I got that done before I could have probably even contacted a TA - whose phone may have been constantly busy because others were calling their TA!
Trip to Vancouver - Hyatt employees had picket line outside; front desk said we had to move to another hotel; I talked the front desk employee into letting us stay because the location was far superior to where we would have ended up. We were two of about 10 guests in the hotel. We got wonderful service! No, I didn't feel guilty about crossing the picket line! Point is that we didn't need to call a TA.
On cruises I've seen people flooded out of their rooms by sewage (Holland American on two cruises!) only to be told the "ship is full", we can't move you! No TA could solve that problem! So the TA gets a "Special Gift" for the poor traveler - that didn't solve the problem! Besides, the traveler can get a "Special Gift" themselves by asking.
There is no TA who can spend the amount of time that I do researching my trips & to know my moment by moment mind changes! I might begin thinking I want to go to Rome, but then my own research changes my mind - a TA wouldn't know that.
There is no TA who can be available 24/7. When I want trip changes, I want it now - I can do that. When there is a problem on the trip, the TA may not be available. Besides, there is not any problem that can occur on a trip that I cannot take care of; no problem that would "require" a TA. No TA has a magic bullet to solve travel problems.
Sorry if I went on too long!

I'm sure you can tell that we began our traveling by using TAs. We soon overcame that fault. My motto is, "All problems are just a solution waiting to happen." I'm capable of my own solutions without waiting for a third party to make my decisions, & I never get upset, even when I don't get the answer I want - just go with the flow - makes life so much more enjoyable

. And, I don't need a TA for that!