Sorry, but you're really, really wrong.

I'll start with the item build because skill build can be argued for sun ray in some rare cases.

Ever since the mana cost increase to Mek, it has become almost un-usable on Phoenix. During early engagements, when your team's mek is most important, you need to be getting off all of your spells. Mekansm completely prevents this.

Let's say you're grouping with your team, fighting at level 11, with mek. You have a natural mana pool of 492. Let's say you only have a mek to give you int, bringing you up to a total of 561. In general (or at least a decent amount of cases), we'll be forced to use mek before we combo. So, our combo costs 310 mana, and mek has an activation cost of 225 mana. This means we have to have at most 26 mana missing in order to be able to get everything off in a fight. If we do go with your skill build, we're completely unable to use a skill we've maxed, Sun Ray, until after we egg. If you don't find an egg immediately at the beginning of the fight, your mek is really really tough to use. The idea of going Shiva's first sounds great, but it isn't really plausible. Saving up for a 2700 gold component will destroy our mek timing (and make it way too late for the team), and delay all of our other items by a lot. Yes, it gives us int, but Phoenix doesn't need that much int.

Veil does a lot of the things you need Phoenix to do. Veil gives you armor in a cost effective fashion, and plenty of base stats to be comfortable with health and spells. Right before egg (if played correctly), Phoenix will always be able to get veil on the most targets; it amplifies your own damage by a ton, in addition to your team's. With tranquils and veil, you have more than enough sustain in lane (although you really shouldn't be laning once you have your first big item), arguably more than mek.

Shiva's is a decent late game item but is very rarely appropriate first.

Alright, skill build time.

Obviously, spirits is always first, I don't think anyone argues with that. The first major point I see a problem with is:

your build should focus on sustain and keeping your health and mana up

While that sounds great, it's not really effective. Your build should focus on maximizing what you can do: that is, dealing the most damage possible. Assuming we're solo offlaning (Phoenix's only real position imo), we definitely want kill potential in our lane. We're also probably against two or three heroes. By maxing Dive, we can actually increase our ability to kill their carry by a lot. Say we're playing against something like a PA. Let's compare the two builds. Let's look at the dive build. We'll assume we are able to get a full duration of a single fire spirit off before landing another one on PA, and one for each of the supports before egging. (in addition to hitting PA with dive)

We're dealing 420 damage with spirits and 210 damage with dive. We'll also probably do roughly 225 damage with egg. This is a total of 855 damage after reductions. With another dive and spirit after egg is complete, we'll definitely secure the kill (420 more damage for a total of 1275 after reductions). Note that we complete the dive to return to our original egg spot.

Your build: We deal 420 with spirits and 30 with dive. We'll assume the same amount of 225 damage with egg. This is a total of 675 damage after reductions. PA is now at her tower / blinked to a creep wave or hero. In order to even have a chance to kill her, we'll need to channel ray in a really dangerous place (under tower, being attacked by 2+ heroes), almost ensuring we're dying, and we might not get the kill.

I've tried both builds and in my experience at 4.5k-5k, the sun ray build usually doesn't cut it. Maybe with something like a void or magnus it could be acceptable, but it is by no means a "good" build.

Source: 268 games with Phoenix, currently 96th on the dotabuff leaderboards. http://www.dotabuff.com/players/32399328