They certainly weren't for protecting the Enterprise from the radiation (wouldn't it have been better not to stretch them around the barge in that case?)
Yet if the order was
given offscreen to reset the shields to surrounding the Enterprise
only, the episode would play out just as we saw. The best possible way for Riker to proceed would have been to create two shield bubbles: one around the barge, to keep the radiation in, and one around his own ship, to keep radiation out. The barge bubble would have been vital as long as they were near the planet, and useful but not vital later on. Alas, creating two shield bubbles with one ship doesn't appear possible in the Trek universe.
I believe in the above transcript, LaForge was simply stating their current situation while thinking what options were available to him in regards to the tractor beam. But it can also be looked at as being a case that they had one system (a tractor beam) operating within another (the deflector shields) and that latter was having an impact on the former.
Indeed, we could argue that LaForge would in all scenarios have a need to constantly ramp up the shields, and his only option for boosting barge integrity, the use of a stronger tractor beam, would conflict with this. That is, the need to ramp up shields was not directly related to Riker's demand for greater towing integrity.
If that was truly the case, it really wouldn't have been necessary to get rid of the barge. They could have merely positioned it at any point clear of the planet and left it there indefinitely.
Quite so. But long dissipation time is not a sufficient
rationalization for why they had to tow it all the way to the sun. We have to invent something stronger to justify the odd towing decision; even with a half-time of billions of years, the barge could always have been left floating at a spot that did not call for the close attentions of the E-D and her vulnerable crew. After all, the barge was only a danger to the planet after settling on a low orbit; any other orbit would do just dandy to allow Riker to cut off the tractor beam and go rescue Picard.
no irradiated zones or spacelanes
The barge was a danger to the planet at a distance of, oh, let's say a thousand kilometers by the visuals, but we can pick five thousand as well. Leaving a zone ten thousand kilometers across somewhere within the system solely reserved for the barge would not affect traffic in any way - it would take a cosmic coincidence for any other spacecraft to ever enter that volume, and even if they did, they could always sail out of it before any harm came to them.
The basic premise of the episode, unfortunately for the writers who obviously wanted something else, was that the barge was harmless. It would remain harmless in any location other than the low planetary orbit; indeed, it had remained harmless since ancient times until ending up at that orbit, and obviously it wouldn't reach another dangerous orbit ever again, what with the propulsion systems gone.
Indeed, we have to wonder why the barge originally established this harmful orbit, supposedly using the last of its engine power (even if the main reactors had been shut down 300 years prior). Was this for sinister purposes, a "dirty bomb" attack that failed due to rusted-out hardware? Was it an industrial operation misperformed by an out-of-date automaton, a harmless cargo transfer maneuver intended to have taken place in another star system millennia ago? Did the vessel perhaps originally carry a beneficial cargo that had gone sour and killed her crew, or had gone sour because something had killed the crew? A simple "distant aliens get rid of waste by immorally careless means" story doesn't wash, because the ship could simply have been sent to the local
sun then - and if that mission failed, there'd be no mechanism by which the ship would then proceed to orbit a faraway planet.
If we're to do the thinking the writers neglected, we could just as well theorize that the barge was launched by the Gamelans themselves - either centuries prior, after which she was forgotten until she looped back due to a programming glitch (or started radiating because the originally harmless cargo rotted somehow), or then fairly recently, and the Gamelans just deceived the Federation into doing their dirty work for them...