Let's consider some possible solutions to the scenario "I need to do some web stuff":
- Hire someone else to do it
- Use an elaborate framework that magically transforms non front end stuff into front end stuff (html, css, js)
- Do it yourself
We will ignore #1 because we're awesome like that. We're left with two choices. Which to choose, which to choose...
#2 is enticing. It means you can stay in your comfort zone, which is quite comfortable, especially if you added a slushy machine and some couches. But let's consider what happens to the framework you're using:
- It bugs out
- It gets outdated
- It doesn't fully match your expectations
- Any other software-related problem.
You're a dev, so it mustn't be hard to consider all the possible ways a product (especially a library) can break in many spectacular ways, ripping your sofas and toppling the slushy machine, painting everything in bright magenta.
In any of those scenarios, you'll have to come back to reconsider the options discussed in the beginning of the answer (only this time replacing the framework in #2), with an added 4th option: Try and fix it on a micro level. In other words, learn the web-stack in a shallow way, only necessary to hack together a solution to that specific problem.
Is it worth it? Depends. You may believe that the framework will never fail you, and you might be right. And you might be wrong.
I propose a hybrid solution: First, learn the web-stack. You don't have to spend a lot of time on it, you don't have to be l33t h4x0rz like that 14 year old from down the street who can add glitter to MySpace pages, you just need to have a basic knowledge of what's going on. Then, if you see that it's the best scenario for you, choose a framework.
Now your comfort zone is a little larger. It might even have a TV or an ABBA: Greatest Hits album proudly on display. Now if something breaks, you'll know how to fix it. Now you have a choice. And having a choice is always better than not having a choice.