I haven't done any research on this, but from this video
it appears Finland had built hard taxi strips to the sides of the highways they planned to use for air strips. They can tow the aircraft over to dirt parking areas, but they don't fire up the engines unless they are sitting on a hard surface that looks like it's been swept to standards someone with severe OCD would approve of. Building those sorts of aprons around highways so aircraft without taxi inlets can operate from the highway takes pre-planning.
I don't know much about the specific design of the Gripen, but I do know that Sweden had the sort of war Ukraine is fighting now in mind when they designed the plane. I assume Saab took the problem of FOD into account.
Here is another article with a US F-16 pilot weighing in:
https://eurasiantimes.com/f-16-fighters-jet-sitting-ducks-for-russian-missiles-us-air-force/
The Ukrainians have probably been pushing for F-16s because they are the western jet they are most likely to get. At least three European air forces have surplus or will soon have surplus F-16s as they transition to F-35s. Those governments have probably been making noises for a while they would like to donate those to Ukraine if the US gave permission.
The Australian F-18s are tied up in some unknown red tape and Sweden has not made any noises that they have many Gripens to give away, so Ukraine campaigned for the fighter they could get.
The F-16 may be the most vulnerable plane to FOD out there. The inlet is only 30 inches above the ground (about 0.75 m). The inlets on the F-18 are about a foot higher (about 30 cm) and set back from where it is on the F-16.
I want Ukraine to be successful, but I am concerned Russia will be able to keep the F-16 bases shut down. They don't even need to hit the runway, just get debris on the runway. That could happen if a drone is shot down over the base. Keep up a flow of drones and Ukraine will have to keep shooting them down and will have to cob the runway again after every attack in case drone fragments of AD ammunition fragments got on the runway or hard stands where they warm up engines.
The Me-262 suffered a similar problem. When they got airborne and up to altitude they were hard to stop, but they were very vulnerable when landing and taking off so the Allies kept fighter patrols near the known Me-262 bases. The Germans had to operate piston engine fighters to try and protect the Me-262s when near the base. The Me-262 was particularly vulnerable when landing. The engines would flame out if the throttle was moved too quickly, so when slowed down for landing, the pilot was committed. If a P-51 jumped them, there was nothing they could do except pray they got down OK.
General Adolf Galland fell out with Hitler in early 1945 and ended up ending the war commanding a unit of Me-262s made up of other experienced pilots he could scrape together. Just before the end of the war he was jumped while landing and just managed to get his plane down and get out before it burned up. He finished the war in the hospital.
The Russians will put a maximum effort into trying to keep the F-16 bases as shut down as possible. They don't have the ability to have fighters loitering around the Ukrainian bases, but they have other things they can do. Along with constant harassing attacks they can also position their MiG-31s to watch the area around the known F-16 bases and shoot down anything they see near the base. The Russians have an extreme range air to air missile that is intended to be used against AWACS, but they have been using them to target Ukrainian aircraft.
Russia’s MiG-31 Crews Are Shooting At Ukrainian Pilots From A Hundred Miles Away—And The Ukrainians Can’t Shoot Back
If the US were drawn into the war, they would arrive with overwhelming air power flying from bases that are well out of range of Russian attack. Additionally because NATO has had decades to prepare, there are dozens of different airfields in Europe the NATO F-16s could operate from in the event of a war with Russia. All the facilities for F-16s and other NATO jets are already there and waiting.
Ukraine's air force is a very small effort compared to what the US can bring. The US can bring a force with a wide array of weapons to neutralize all Russian air defense and knock all Russian aircraft out of the sky anywhere near Ukraine within a couple of days. Ukraine is never going to have that kind of air power. Even if the west gave them enough aircraft and trained enough pilots from scratch they don't have the ground infrastructure to support such a force.
Ukraine's air force is like the raiding force that went into Belgorod oblast and the US's air forces are like a massive army. A raiding force can do damage and freak out the enemy, which that force did, but to take and hold ground you need numbers. In the air to gain and hold air superiority you need numbers. The Ukrainians can deny air superiority to the Russians, but they have no hope of gaining it themselves unless something happens to the entire Russian air force. Which is probably not going to happen.
The F-16 is a premiere light weight boxer, great in the ring, but maybe not so great in a street brawl. Ukraine needs a good street fighter that can fight dirty and work in unpredictable ways.