Unlike most people (it seems) I have actually managed my notifications pretty effectively which means they all matter to me. However, for whatever reason, I often miss them. I don't feel the vibration (iPhone 6+ vibration seems utterly pointlessly weak) or hear the sound. A tap on the wrist and a glance at my wrist to see what's come up and decide if I actually need to act on it is 1000x improved over constantly pulling my giant phone out of my pocket ever few minutes to be sure I didn't miss an emergency message from my wife or a facetime call from my daughter, or one of my VIP's emailing with an emergency issue that needs my attention right away.
Basically the canonical use case.
Furthermore, when cycling, I don't like to have my phone out. I prefer to stow it in a frame bag or just covered up in my jersey pocket and getting that out is a big pain compared to a normal pocket grab, plus, it's always something that has to be done very fast, whether in the moment I'm stuck waiting at a light, or actually on my way, I can't be spending more than a couple seconds which means I'm going to rush which means the chances I'll drop the phone from my partially gloved hand is way higher. But, the only thing I need to be doing is double checking that I haven't received any important notifications, or see who is calling me right now before answering on my BT headphones (or more likely, just ignoring the call.)
People depend on me. I have the ability to be responsive which in some cases saves projects, and in less common cases, saves lives.
Frankly, it would be nice just to be able to quickly see what music has come up on shuffle, or pick a different playlist when my mood strikes. I usually pick a playlist before starting a ride but, sometimes it just isn't working for me or I decide to ride longer than the playlist and need to get something else started.
For me, the Watch is a 1000 paper cuts kind of deal. Many tiny uses where no single one is critical, but, in the grand scheme of things, and coupled with my willingness to plan and prepare everything to maximize the value (such as is required when doing, say, GTD planning style), I expect to derive quite a large amount of value from this device.
However, just to offer a counter view, I think if you're too lazy to even bother managing your notifications currently, you're not going to be willing to do the leg work to get the most out of the watch and probably won't be nearly as satisfied with it as I will be. Tools require effort to master and maximize their utility. So much capability is squandered on the iPhones we're already carrying by many people (like people forgetting what they went to the store to buy even though their phone can literally take a list by dictation, or forgetting to get something done even though they could've just asked for a reminder) and I'm suspecting that in the case of the watch, things will actually be even worse.
