If the filmed element had been in storage for the years since it was shot, like TNG, they would've held up fine. Like TNG, they would've had to done things like phaser beams and torpedoes in CGI.
One, if the original film elements still existed, re-compositing them would definitely result in an improved image, but I doubt it would hold up as well as the motion control work from Star Trek: The Next Generation
does. That's simply the difference that twenty years makes in visual effects.
Two, if the original film elements still existed, there would be no reason to recreate the phaser and torpedo effects using CGI. That's been done on Star Trek: The Next Generation
because that series created those effects on video; everything on the original series was done on film.
A shame the elements were not preserved, but hardly surprising, given the series' age. Also, although I'm not crazy about the CGI enhancements, few of them are as bad as the image you've posted. It's a bit harsh to condemn that work based on the worst example from it.