You can certainly use JQuery as your API base if you're willing to take the hit on performance and a few hundred KB download, and are willing to take that hit on every project you write.
The problem is that this shuts you out of a lot of hot, emerging markets that can be quite lucrative. You will never work for Google (as a front-end engineer) if you only know JQuery and not the native DOM APIs. Your mobile HTML5 apps will suck and will lose out to native counterparts in the app store. You're at a disadvantage in any competitive web market where people bounce from the website if it's too slow (there are more of these than you think).
If you're willing to limit yourself in this way, sure, go for JQuery. There is still a pretty booming market for Intranet apps or progressive-enhancement mostly-static sites where JQuery is just fine, and it provides a nice productivity boost for those use-cases.
The advantage of polyfills is that they give you flexibility and let you push the edge of technology today, and then they don't become obsolete tomorrow. As the web evolves you just get rid of the polyfill and you already know the latest & greatest of tomorrow. That lets you push into the emerging new markets that can be quite lucrative, at the expense of actually learning the (sometimes hard-to-use) APIs on the bleeding edge.
That makes a lot of sense especially in areas where you are competing for people's attention. If you aspire to being a front-end engineer it'd be silly not to know the DOM APIs inside and out, especially now that browsers have such nice dev tooling.
But for those aspiring to create big things another approach is to find a niche where you can offer something exclusive that people want. Thefacebook offered something that students would have put up with > 1s load times to see that they couldn't reliably get anywhere else. http://en.wikipedia.org/wiki/File:Thefacebook.png
The problem is that this shuts you out of a lot of hot, emerging markets that can be quite lucrative. You will never work for Google (as a front-end engineer) if you only know JQuery and not the native DOM APIs. Your mobile HTML5 apps will suck and will lose out to native counterparts in the app store. You're at a disadvantage in any competitive web market where people bounce from the website if it's too slow (there are more of these than you think).
If you're willing to limit yourself in this way, sure, go for JQuery. There is still a pretty booming market for Intranet apps or progressive-enhancement mostly-static sites where JQuery is just fine, and it provides a nice productivity boost for those use-cases.
The advantage of polyfills is that they give you flexibility and let you push the edge of technology today, and then they don't become obsolete tomorrow. As the web evolves you just get rid of the polyfill and you already know the latest & greatest of tomorrow. That lets you push into the emerging new markets that can be quite lucrative, at the expense of actually learning the (sometimes hard-to-use) APIs on the bleeding edge.