First, I'm going to restrict my commentary to the use case presented: Home-recorded DVDs on a commercial "VCR-like" DVD recorder or DVD camcorder on DVD-R or DVD-RW disc. I am *NOT* going to cover Hollywood-release commercial movie DVDs bought from a store.
Recordings from these type of devices record DVD-standard MPEG-2 codec video in to a standard folder format.
Apple DVD Player can play these "folders" just fine - just drag the contents of the DVD to a folder.
Likewise, Apple DVD Player can play a disc image of the DVD, created with OS X-standard Disk Utility.
Both of these methods produce "perfect DVD copies" - with menu systems and all. In addition to that, it takes essentially only the amount of time to copy the data off the DVD (so you're limited ONLY by the speed of your DVD drive.)
But both of these options produce files/folders that are fairly large compared to other compression methods. Modern codecs like AVC (also called H.264) or even the older MPEG-4, or the newer H.265, can compress a video down to 1/4 the size of MPEG-2, with no perceptible loss in quality.
That is where utilities like Handbrake excel. They read the raw video off the DVD's folder structure, and convert it to a more highly-compressed single .m4v file. This file cannot be read by Apple DVD Player, and doesn't have the DVD menu structure, but it takes a lot less space. (Generally 1/4 the size.) This takes more time, as you're limited not just by the speed of the DVD drive, but by how fast your computer can transcode the file.
But if you're just wanting to "watch the content that's on my DVD without the DVD in the drive," Handbrake or similar are a great option.
And yes, Handbrake has gotten a lot better in recent years. The latest versions even take advantage of Intel's "QuickSync" technology in its latest CPUs to make the transcoding process *MUCH* faster. (For example, using 16 CPU threads (8 physical cores and 8 virtual "HyperThreading" cores,) on a dual-socket, quad-core-per-socket Xeon 5500-series workstation gets me about 15-30 frames per second transcoding 1080p video. But using a dual core Core i3 4000-series with QuickSync, it gets 80-100 frames per second.)