HVAC system has freon leak and professional are suggesting a new system.

I got in touch with a company that came highly recommended by some pretty wealthy people. I had them come out and look at my system originally because it kept freezing up. They put 4lbs of freon in it and left.

It stopped freezing up and was cool for a few days before it started to just stop cooling the house. It was blowing air and wasn't frozen, but the air wasn't cool. They came back to the house and put 12 lbs of freon in it and found a leak in the attic and repaired it.

That was Wednesday of last week. Saturday the temp started to go up again in the house and the HVAC was no longer blowing cold air. I called them back and left them a message for this morning. He called and told me that he found rust in the system last time he was over there (house is only about 12 years old) and told me that leaks are very hard to find and expensive. He is now recommending that I get a new system.

I wanted to post here to see if this is normal. The guys were there for only long enough to let the system thaw and put in 4 lbs of freon the first time out. Last Wednesday they were there for 2 hours. Is this long enough for a proper diagnosis of "pay nearly $5k for a new system" or should I have them keep looking?

I appreciate any help I can get.

UPDATE - I went with a replacement system after they came out today and found that the compressor was bad. It was either $2k to replace the compressor or $3,800 for a replacement system plus they're subtracting what I've paid for the first visit from this total. I appreciate the responses!