Do you think that the F-16 have the potential to be a game changer?
No.
Individual weapon platforms need to fit a proper cohesive doctrine as a small cog in the overall fighting strategy of a military. Rarely do individual 'wunderwaffen' work in a broad battlefield context (barring exceptional circumstances, like African tribesman armed with Spears and Shields charging lines of Maxim Guns). The F-16 is a very small piece of the overall NATO doctrine developed in the 1980's called Airland Battle, and later modified to something called 'Full spectrum dominance'. A singular fighter jet, in low numbers, no matter how good, is unable to shift the battlefield on its own without a full integration to its own battlefield needs with specific designs to fit those needs. Sorry if this sounds like word jumble, let me try and explain with examples.
The F-16 was designed as the 'lo' aspect of the 'lo-hi' calculus in the US air force. The 'hi' being the F15. Hi-lo is basically the idea that you have a smaller, limited amounts, of very high quality aircraft that is designed to take control of the skies in rapid time followed by the 'lo' (cheap, more disposable aircraft that have a wider utilization use at more bang for buck), which then supports ground troops. In Modern times the 'Hi' aspect of the US Air force is the F22 (and in the future, the NGAD/FA(XX)/whatever the new air force one is designated as), with the 'lo' being the F-35.
From a strategic perspective, the first and most important mission is SEAD/DEAD (Suppression/denial of enemy air defences). This is a combination of Air superiority 'Hi' fighters (F15C, F-15E/EX, F-22), stand off munitions (TLAMs, JASSM's), anti-radar assets, stealth penetrators (B-2's), going at full operational velocity, before further degradation is completely with more vulnerable assets with higher firepower (B1's, B52's, etc). Once this phase has been completed, the 'Lo' aspect of the mission profile really kicks in. F16's providing mobile air support, air cover, CAS missions, Tactical bombing etc etc, all the while the sky is dominated by the 'Hi'. That's not to say the F-16 cannot do Air to air combat missions, it's very good at doing so, especially since Block 72.
The key part to all of this is real time battlefield command and control. F-16's have great electronic suites, again especially since the latest blocks, but it's not enough to dominate a battlefield on it's own. It requires AWACS and AEWC&C as well as ELINT aircraft in the sky, after the initial SEAD/DEAD phase to provide real time battlefield intelligence to all the constituent parts. The real important part here is command, control and intelligence. US battalions have dedicated, fully trained, communications units with top range C3i equipment to communicate seamlessly with all the other assets on the ground, in the sky, and beyond. F-16's can be raised into the skies to provide CAS/Tactical bombing support and be given real time missions that are not briefly until after take off, with real time intelligence being communicated to the squadrons to assist where it need be. Again, communication is king.
A unit that has been bogged down, suppressed or needs general fire support, cannot make a request, wait for it to be passed down up and down the chain, until a fighter is scrambled, sent to the location to provide assistance. It might be too late then. One of the F-16's job is to provide real time support when and need be. One other really important thing here is "battlefield intiative", which is really dependent on a very well organized, high moral and very well trained NCO group. You cannot wait to escalate up the chain or to ask permission, you have to make decisions in real time, on the spot, without asking for permission. This is what NATO (not all of NATO but western europe and USA) really excel at. Decades and decades of a culture of NCO initiative, fostered by a no-blame culture and instilling that belief in NCO's.
I can give an anecdote from 2003 Iraq War invasion. A Sniper gets bogged down North of Basra and he is under fire from Iraqi's troops. He and his spotter cannot escape and are completely suppressed. The spotter contacts his CO HQ requesting artillery support. His CO HQ responds that there are no artillery units within range of his position to provide support. Rather than escalate to his superior, the radioman at the CO HQ immediately contacts the Air force command to ask for assistance for any assets in the vicinity. The answer is no, but the Air force radioman asks for the Ground force radioman to wait, as he contacts an E-3 Sentry patrolling in the skies above. The E-3 Sentry confirms to the air force radioman that there are naval assets in the region, and in turn the Ground force radioman contacts the USS Theodore Roosevelt with a request for assistance with broad co-ordinates. The USS Theodore Roosevelt radioman contacts an in air E-2 Hawkeye, who commands two patrolling F-18 Hornets to the location of where the sniper is being suppressed. 3 minutes later the F-18 hornets arrive and bomb the troops firing on the Sniper, allowing them to escape.
The entire chain of: Sniper team -> CO HQ -> Airforce -> E3 -> Airforce -> CO HQ -> USS Roosevelt -> E2 -> F18: Took a grand total of 88 seconds. 88 seconds to communicate between three different branches to command and control air support for a sniper team.
Now, why won't this work for Ukraine? So many reasons:
1) No 'Hi' in the calculus to control the skies.
2) Limited SEAD/DEAD to supress and destroy the air defense assets. Ukraine would have to use F-16's to do this, or Mig29's or SU-25's which are not suitable for this purpose.
3) F16's exist to be the 'Lo', high in quantity and allows for tactical sortie flexbility. Ukraine does not have anywhere close to enough to achieve this.
4) No C3i infrastructure to allow for tactical and strategic level asset communication in seconds.
5) No Battlefield intelligence platforms like E3/E2, ELINT or command and control assets.
6) No homogenous NCO culture that allows for on the spot decision making without hesitation.
7) All these factors mean the F-16 will be an order of magnitude less effective in Ukrainian hands than it would be in NATO hands.
If the anecdote was transposed to Ukraine it would go as follows.
Sniper calls in for air support, there are russians around his position. CO HQ says there's no support. Sniper begs. Radioman says he will ask his superior office. Superior officer says he will make a call to the Air force regional commanding officer. Air Force commanding officer has no idea what assets are available. Says feck it, lets scramble a jet (doubt he would even do that to be honest). Jet takes off into the air. By the time it arrives, Sniper is dead. Plane is now intercepted by AA missiles. Plane shot down.