"Better job" is subjective. We certainly get lots of questions like

• Why does this camera generated JPEG look better than the software generated one?
• Why do RAW images look worse than JPEGs in editing programs?
• Why do my RAW pictures look fine in Lightroom preview but become faded when exported?

which by their very existence show that many people like the results they're getting out-of-camera. RAW conversion certainly does not automatically result in "better" images, at least not for some universal definition of "better".

However, every RAW program is different. It very may be that the default settings of some such program match your preferences better. (Or, the settings with a few tweaks which you never again touch.) If that's the case, then, sure, that will be the "best workflow" for you. But there's no universal definition of better.

I am willing to give more time for the algorithm to perform the same outside of my camera.

It sounds like you're thinking that the computer may allow more sophisticated or longer-running conversion algorithms, due to the bigger CPU and additional memory, thus getting more detail or better color or something. This isn't actually the case — computers allow more flexibility, but the hardware and software in the camera are finely tuned and optimized to be really, really good at this specific task. Fujifilm, in fact, recently released a feature which lets you use a USB-connected camera as a sort of co-processor in RAW conversion, sending the files to the camera to use its conversion pipeline. That is, the tuned processing in the camera's dedicated hardware is so much better than a general-purpose CPU for this one task that it's computationally worthwhile to send the files off-computer and back again.

In general, the real advantage of RAW is this flexibility. There is no one set of settings that will be "best" for every image for most reasonable definitions of "best". Having RAW files lets you decide that after the fact, including comparing different software and algorithms for the particular image.

However, with most cameras, you can get a good chunk of that flexibility by saving in RAW+JPEG. You can use the JPEG files in the common case, and use in-camera after-the-fact RAW-to-JPEG for fixing white balance errors or similar — and then you always have the RAW files if you have an image you really decide you want to give different treatment to.

(And, I'd encourage you to store the RAW files after the fact. Storage is relatively cheap. If you have Amazon Prime, you have unlimited online storage for images including RAW files; might as well stash them there in case you decide you want 'em later.)