I have a 1999 GMC Denali with about 123K miles. Loose steering

Had the same issue and looked for answers all over and they say to change the steering sensor in the steering shaft under the dash right next to the brake pedal and also the EVO sensor on the power steering pump. That all sounds great and by the way I had changed out all my frontend parts as in tie rods, ball joints and ect and yes it still had the loose steering problem. I am not sure in your condition do you have to add power steering fluid due to a slight leak? If so your problem is a bad hose yes I mean a bad pressure hose, which in my case I had a leak there but it should not really affect it to much but I was wrong this does affect it in this case and I did replace it and the whole system is back to a nice solid steering at high speeds and all under control. So make sure you have "no" leaks at all before changing those sensors.

It's, to my knowledge that the intermediate steering shaft is gone bad. Specifically speaking about the (rag) joint that bolts to the steering box itself. Easy fix, available at most all parts stores and don't require any special tools and can be done by even the most inexperienced person with a mild knowledge of mechanics and basic tools