It's complicated. If you watch traffic in the Corpus Christi ship channel, from Port Aransas on in, sometimes they use tugs. Spinning a big ass prop in a narrow channel with an 18 knot crosswind is a tricky proposition. Using the tug comes with its own cost, problems and risk. Is it going to connect with a cable? is it just going to ride on one side of the bow and push/pull? Those tug guys get killed from time to time because that job is dangerous. Hooking up tugs to everybody coming and going isn't a guarantee.
I guess one could be thinking "rescue tug" that just sits there by the bridge and when something goes awry they go lasso the ship, throw it into reverse, and save the day. It would be fun to watch but I doubt it's a realistic plan.
Data point - internet says wind was 6mph, gusting to 17, at 2am. I'm pretty sure that would be considered almost calm/very mild for this operation. Wind was not a factor. They had momentum and lost steering / power somehow.