If knowing how far from the hole really detracts that much from your enjoyment of the game, well I feel for your loss. But I just can't see the appeal, myself.
Then again, I'm a person who would rather play one course five times than five courses once. To me the pleasurable part of golf is knowing exactly what I need to do, having a clear mental image of where I want the ball to land and how it will bounce or roll from there and then attempting the shot I'm imagining. Once I've played a given hole quite a few times or once I've played it to exactly the same hole location even two or three times, any mystery about "dead ground" or "visual deception" or those other beard-puller's pleasures are pretty much out the window.
I had a shot yesterday with 104 yards to the hole. I knew the distance, I knew that anything more than 8 yards past the flag would bounce over the green, dead. I knew that anything more than 5 yards short would fail to stay on the upper tier and would end up rolling 30, 40, 50 feet away leaving a tough 2-putt. I opted for playing a 100-yard shot and it came up just short, paused for a second, then slowly trickled all the way back to the front of the green.
How would that experience have been improved if instead of knowing that it was 104 to the hole I just eyeballed it and knew it was somewhere between 98 and 110 yards? I prefer knowing that if I can land a pitching wedge shot in that narrow little window I'll have a makeable birdie putt and if I miss that known window I may not make par. If I did not know the exact distance the prudent play would have been 20 feet left of the hole, take plenty of club and play for a long putt from the back fringe. Without knowing the distance my chances of a makeable birdie putt go from 1-in-4 to maybe 1-in10 or 1-in-20 just because there's not just a perfect shot required but a perfect shot and a perfect guess as to distance.
In the end, it could down to whether guessing distances is a pleasurable pastime. As I said, if you really get off on guessing distances then I hope you're able to somehow insulate yourself from the near-ubiquitous yardage information that's a normative part of the game today. But it's a niche desire that doesn't necessarily get catered to in every round of golf.