Why do I need to use a popular framework?
Frameworks have several advantages:
You don't have to write everything. In your case, this is less of a help because you have your own framework which you have accumulated over the years.
Frameworks provide standardized and tested ways of doing things. The more users there are of a given framework, the more edge cases that have been encountered and coded for. Your own code may, or may not, be battle hardened in the same way.
Others can be recruited onto a project with a standard framework and have access to the documentation, examples and experience with that framework. Your own snippets may or may not be fully documented or have examples of use... but isn't much chance that others are comfortable with them initially.
EDIT:
With regards to your idea of packaging up your own framework, the benefit of cleaning it up for public consumption can be larger than the benefit of getting others to use it.
The reason is simple: you will have to re-evaluate your assumptions about each component, how they fit together and how clear each piece is to understand. Once you publish your framework, your success will be strongly dependent on how easy it is to get up and running with.
Big wins with little effort are essential for adoption (those wins will encourage people to delve further into the framework). Ruby on Rails in an example of a framework that gives such big wins with little effort, and then has hidden layers of features that would have overwhelmed someone just getting started. (The question of the quality of RoR apps is not the point, the point is about adoption speed).
After people adopt a framework, it is about the ease of continued use. Little details like consistent parameter use patterns make all the difference here. If one class has many parameters on every method, while another has setters that are expected to be called before invoking methods, you will lose users because they can't get a "feel" for what is expected in a given case without resorting to the documents.
If both ease-of-adoption and ease-of-living-with issues are addressed properly, you only have to get lucky for people to adopt your framework. If those issues are not addressed properly, even an initial interest in the framework will wane quickly. The reason is that there are many frameworks: you will need to stand out to gain the advantages of having others using your kit (as they rightfully are as wary of your framework as you are of others).
Here's another reason not to create your own framework. Linus' Law - "Given enough eyeballs, all bugs are shallow". In other words, the more people who use a given framework, the more solid and bug-free it is likely to be.
Have you seen how many web frameworks there are for Java? Back in the day, it was fashionable for any half-decent developer/architect to write their own custom web framework. And at the end of the day, 95% of them looked like a custom implementation of Struts (the most popular Java web framework at the time). So they basically created a Struts clone that was: 1) proprietary; and 2) not as well documented and tested.
Let's face it - writing our own customer framework is fun, but what happens next? It becomes a maintenance burden to keep up with the framework yourself (or the poor soul who replaces you). And maintaining software is much, much more costly, especially when it comes to custom frameworks. Is the company in business to solve domain problems or in the business of maintaining frameworks?
I forget who said it, but I once heard a great quote - "The first rule to creating your own framework is: don't". Somebody else has probably gone through the effort of doing so and probably done the same work you would have done. Save yourself the time, effort, and testing.
There's many comments here as to the advantages of using a framework, and certainly I think in a good many cases they are perfectly correct.
HOWEVER
All frameworks come with the downside that they have a domain of problems that can be fitted into them. If your problem is well inside the scope of the domain then using a framework isn't an issue, and most of the time it's readily apparent if your problem is well outside the domain so you don't give it a thought. Issues arise when you try to force a problem into a framework that it just doesn't quite fit into or has some unusual non-standard feature - in which case you complete 90% of the code really fast then spend all the time you've saved figuring out how to bend or extend the framework so it can accomplish some obscure requirement. Because in these case your solution/extension has to plug into the framework it can often be more difficult to code than if you'd come to it independently.
In the wrong circumstances this can actually be disastrous. For example if a client asks for a project that you believe will fit into a framework solution and you quote accordingly, then after completing 90% you find the gotcha then you can be really up the creek, especially if it's some feature that the client is insistent upon (and it always is). These issues tend to arise because it is not always apparent from the word go where the gotchas might lie, particularly if you're using a framework you are less familiar with (and you have to from time to time).
This is really the same problem as arises with deploying any third party software in a project. Myself from experience I have no qualms about using frameworks or similar, but given the choice I will always go for the lightest, thinnest, wrapper I can find that will do what I need. That way I gain the advantages, whilst knowing that if issues do arise (and they are generally less likely to with a thinner wrapper) then figuring out how to work around them is likely to be simpler than learning an extensive code-base to the point where I can safely modify it.
The framework code is likely to be well-tested and relatively free of bugs. By using it you save yourself time testing/maintaining your own code to do the same thing.
And any time saved is good. Laziness pays off in programming.
One thing that you will be missing out on is all of the Validation that goes into a popular framework.
Your routines simply don't have the same exposure that the popular libraries have.