I work with databases in my day job, so Lightroom was second nature to me when the first betas of v1 appeared a few years back.
I've also been using Photoshop for nearly 20 years, so I'm hardly immune to its charms.
With Lightroom, I keyword everything I shoot. I can find anything instantly. I can rate and organise which pictures are going to make the cut much more rapidly than anything else I've tried.
For applying a white balance correction across seventy photos, it's
way quicker than anything I could do with Photoshop. If I took a hundred photos in a day, it would take me several hours to work my way through them before. Now I can tag
and do the PP in an hour or so. Based on my recent history, Lightroom suffices for 99.5% of my editing needs - if I could stitch panoramas using Lightroom alone, I think Photoshop would be nearly redundant.
If you only shoot JPEGs, and not too many of them, do a couple of tweaks and save back as a JPEG, then it may well not be for you.
Non-destructive editing has its advantages; the most obvious being that you can go back to any point in your editing history and change it.
If you shoot RAW, then with my 12.8 Mpx 5D, a single-layer 16-bit RGB TIFF file is 70-odd MB (which is how I used to keep my 'master' files after PP in Photoshop before Lightroom) vs about 12.5 MB for the RAW.
With about 75,000 images in my Lightroom library, if I'd converted every one to TIFF, that makes the difference between needing 1 TB of storage and 5.25 TB. Even at a lower keeper rate and deleting the rest, that would nearly be enough to justify the cost of Lightroom alone, especially when you have to consider backing that lot up (and simple mirrored RAID as a safety net). Go back to the cost of storage even a couple of years ago, or if today you're shooting with a higher pixel count, then a handsome saving can be made.
If you keep layered Photoshop files to allow further adjustments to your edits (see first note above about non-destructive editing) you and multiply the storage costs still further.
It has some weaknesses. Notably, there's currently no API to allow other developers to hook into the RAW processing engine, so if you need to take an image out into something like Nik Silver Efex Pro for a nicer b/w conversion, it has to make the round trip via a TIFF file, which obviously interrupts the non-destructive editing workflow.
I could think of other areas it could be improved (wishlist #2, to allow the substitution of a different RAW processor such as RPP or DXO in place of Adobe's Camera RAW engine; #3 allow local adjustments of anything you can do globally, such as white balance, #4 a better clone tool, etc.) but it's pretty useful tool for me as it is.