There is a book on hiking Whitney that I read that devotes a section to group dynamics and communication. The bottom line: good communication and a clear understanding about expectations is an essential component to hiking with others. If you don't trust your hiking partner, you need another partner. If you trust your hiking partner, but you have different expectations, and cannot reconcile them, you need a new hiking partner. If you trust your hiking partner, and have different expectations, but can plan work-arounds solutions that work for you both, then go for it.
It is true that folks solo hike Whitney all the time. Indeed, the first time I was on Whitney, I overnighted at Outpost Camp, and then solohiked to Trail Camp (with my dog) and enjoyed it (though I did pass some very altitude-sick folks at Consultation Lake who were day hiking). As a first timer going for the summit, however, I would not have wanted to solo hike past Trail Crest. (Now that I have some knowledge of the mountain and have some experience at altitude, I would do so.) People have different comfort levels. Given the disorienting affects of AMS, and the fact that others can really help out (e.g., providing water, encouragement, taking some weight), my own view is that, unless you know the environment and are familiar with altitude, it would be better to go with a partner. I have, in fact, provided water, tylenol, electrolytes, and other support to people on Whitney who were sick on both of my summit trips on Whitney -- some of whom were in my party, and some of whom were not -- as well as on a summit trip to White.
If you are going to solo hike a 14'er your first time around, White Mountain is the way to go, particularly the first Sunday in August, which is an open house. On that day, they open the Barcroft Gate, and you hike a jeep trail 5 miles to the summit, and 5 miles back, 10 miles total (normally it is 14 miles round trip). Nice to have a car with a little bit of clearance to do the dirt road up to the trailhead, though we saw Honda Civics doing it.... When I did it (my first 14'er), I ended up going up to the summit solo when my friend turned around at 13,600 feet. There were so many people up there (because of the open house) that it felt like a walk in the park. If you do go for White, an acclimitization hike the day before in the Ancient Bristlecone Forest is highly recommended -- then sleep at the Barcroft gate that night (no water so bring your own, but there is a pit toilet).
And again, on speed of ascent: Based on my own research (largely using internet sources, but including review of some published peer-reviewed articles, but I am not an MD or researcher), I am personally totally convinced that rate of ascent is highly correlated to likelihood of getting AMS. Put simply, the faster you climb, the higher the relative risk. A slow steady pace will, comparatively, reduce your chances. (I am most definitely a tortoise, and I have yet to experience AMS on a California 14'er, though one cannot get cocky about these things, and I build in a lot of acclimatization on my hikes!)
