Irrelevant is too strong a word. Obsolescent, sure, but the same gun is still in use in the Ukraine war. It's a WW2 design, but the only real deficiency compared to a modern equivalent is range. It only has an 11 km range, while a modern M777 is double that. Note that the M777 isn't a direct equivalent since it's a 155mm gun while the C3 is a 105mm gun, so it will naturally have less range and explosive payload, but the C3 is lighter and easier to handle, more robust, and owing to the smaller shell, has a higher rate of fire.

Another big advantage of the older C3 (and older guns in general) is that they don't give you brain injuries. The idea behind the M777 was to pack a 155mm gun-howitzer into the lightest carriage possible, and to do this they needed to attach a really big muzzle brake to control the recoil, which directs all that overpressure backwards and toward the crew. It's the equivalent of getting punched in the head every time they fire, and a few times is fine, but for prolonged fire they get TBIs.

The light carriage causes other problems, mainly regarding reliability. Titanium, while strong, is weaker than steel while also being much harder to weld. A repair that could be done in the field on a steel carriage might have to be done at a specialized workshop for a titanium one.

My read is that it's mostly due to NATO having standardized all of its artillery to 155mm, at which point old 105mm guns were put in reserve. Then, with the Ukraine war, they probably sent most of the remaining 105mm shells there. Personally, I think it would have been smarter to keep the C3s and put them in fortified bunkers in the mountains to defend against possible US invasion.