In the case of an electrical fire with the dryer, accessing the panel would be difficult to impossible. That DOES happen. In fact, just recently a friend had a heating element flame out, and when it did, it's pieces fused to ground, causing them to stay on. The seals began to smoke, and caught fire. Switching it off did not work, and only her husband's quick thinking to shut off the breaker saved them from what could have been a pretty good house fire.

The setup might not have been anti-code at the time it was done. It is not something I would want personally for reasons the other people mentioned, but I doubt if it has to be a deal breaker. Depends how bad you want the house, I guess. Relocating an electric dryer should not cost a fortune. Moving a gas dryer would cost more.

You'd need a proper disconnect for the dryer you could get to though most people legitimately use the cord-and-plug as the disconnecting means.

The installation of a dryer in front of the panel would never have likely passed inspection but was some kludge done afterwards. Still it's wrong and I'd either make them fix it or have plans of my own to do so.

The NEC does not require updates to existing installations whenever revisions no longer permit any condition that previously was in compliance--- provided that the existing installation is in good condition needing no repairs.
The referenced "inspector" is a home inspector rather than an electrical inspector who works for the governmental agency which has jurisdiction for your location?
Home inspectors often "know" much that ain't so. If it is the electrical inspector, he has the force of law behind him and even if he is wrong, your ultimate recourse in the courts.
Some of the exceptions which cover existing installations are at NEC Article 110-26.
Some earlier editions (than 2014) of the NEC specifically addressed the matter of existing installations. Now the requirements are scattered throughout the NEC.
The dryer is not permanently in place-- it can be moved away temporarily just as could a bucket or box. A fastened-in-place cabinet would be a different matter.
If I was the seller of the house, I would not pay for the changes to be done. The buyer could go elsewhere.

Here is a link that might be useful: Discussion

I argue the installation was never in compliance. Not blocking access to panelboards has been around a long, long, time.

No, nothing precludes you in residences from piling up crap in front of the panel. It's still not a good idea.

You've got leverage if you have a inspection clause.

Our thoughts only count so much. What will your insurance company say in the event of a claim? Especially if the final reports indicates dryer
hinderance?

I'm pretty sure the insurance company won't give a darn.
The bigger issue is how the thing is vented....that's going to cause more issues than the electrical problems.

The reason it's a code violation is because it is a fire hazard, just like the entire NEC, being written by the NFPA. It is called out in your inspection report, therefor you should be able to have the seller fix it. I have still installed panel changes in places that were like this, but they would not pass if the inspector could figure out an appliance was going there. The last time i had this issue, the inspector told me to remove the dryer outlet, and plug the dryer vent hole. And that is how i left it. Turning a blind eye to whatever the homeowner was going to try to do later, although you and me both know that the dryer is going right back in the same place. Moving a dryer or refrigerator out of the way is NOT 'readily accessible'. On an electrical forum people are even giving grief to boxes of various chemicals under the sink getting in the way of pushing the button on a gfi recept, so you could imagine their thoughts on having to move a dryer out of the way.
That being said, the only fire hazard is if your house is on fire and somebody is going to try to get to the panel to kill electricity to the house. Assuming you have a main breaker panel, the danger would be almost nothing since the main is easy to find. If you don't have a main, then it would take longer to turn off everything, but still doable in a matter of seconds. So the danger is almost non existant. However if you hire someone to do work on your panel, as in a breaker fails, then you will have a pissed off electrician, that has to tell you to move the dryer out of the way, just like whenever we have to open a panel at any chinese restaurant, mini market etc etc. Almost every business has nine tons of crap piled in front of the panel. This is the most common code violation you could think of. I would not worry about it, but when it comes to sell your house, i will bet that YOU are going to be the one to hire me to move your dryer circuit, and you are looking at about 5 hundies.

Another potential danger is that reaching over the dryer to reset a breaker you are probably going to be touching the dryer... Which is grounded . Never a good idea to be near a panel box while touching a ground .

The thing about stuff like this is not so much as this is a grave danger but that if the obvious wasn't done to code what is the hidden stuff like. Kind of like an iceberg ... You can only see 1/3 of it. I speak from experience in my house. Every time I touch something I have to spend dollars fixing the last morons mistakes.

And depending on how the dryer is hooked up there might not even be an equipment grounding conductor, it may be grounded to the grounded conductor. This is absolutely dangerous especially on unfinished concrete floors. The frame of the dryer may not actually be at ground potential.

I guarantee you if the dryer hinders the extinguishing of a fire the insurance will give a damn. Here in Ca anyway.