Why EXACTLY is it desirable to generate returns unexplained by widely known factors?

I have a noob and somewhat off-topic question here:
Why is it desirable to generate returns unexplained by widely known factors?

For example:
When doing a regression using the Fama-French Three-Factor model, you generally do not want your alpha to be 0. This does not make much sense to me. While I can somewhat understand that you want low-beta as it corresponds to high-volatility (does it really?), I do not see any reason why you need to avoid having high attributability to SMB and HML.

Some articles propose (i.e. Investopedia) that it is because small-caps and value stocks are inherently riskier (whatever "riskier" in this context means). However, if you can generate better volatility-adjusted returns by incorporating small-caps and value stocks, why do you care whether it is inherently riskier or not?

Excellent question "Why is it desirable to generate returns unexplained by widely known factors?".

In regards to why Quantopian places restrictions on exposure to common factors...

The short answer is because Quantopian chose to make exposure to these factors a constraint. There aren't universal goals and constraints for investing and there isn't a universal 'good' or 'bad' strategy. Because Quantopian wanted to market an investment product to a certain type of institutional investor, we chose these specific constraints. Other investors will have other constraints.

The institutional investors which Quantopian targets often have their own quant teams. They are very capable of crafting portfolios which capture well known alpha factors. Moreover, many of these factors, such as small-cap or value, can easily be invested in simply by purchasing a low fee ETF. In order to sell a product to these target investors, Quantopian tried to construct a portfolio different from what these investors could develop on their own.

Every investor has different goals and constraints. There is not a 'one size fits all' investment/trading strategy. I cannot emphasize this enough. The constraints are obviously different. Retail US 401k investors are constrained with long only un-leveraged portfolios. Some institutions are constrained by how much cash they can or cannot have on hand, or perhaps only US equities. Moreover, goals are different too. Not everyone is looking for high returns. Mitigating risk, and/or balancing return vs risk, is often the overarching goal. But, as noted in the original post, what does risk mean? How is it measured? Every investor has their own definition of risk from volatility, to drawdown, to long-tail (kurtosis), geographic exposure, sector exposure, and the list goes on and on.

So, there is nothing inherently desirable to generating returns unexplained by widely known factors. In fact, unless your specific goals or constraints preclude them, one may want to explore these widely known factors. Historically they generate alpha. If one is looking to enter the Quantopian contest, then you must keep the various exposure results within defined limits. However, if one is looking to develop a trading strategy for other purposes, then perhaps increase some of these exposures. Maybe a high volatility short term reversal strategy works for you. There isn't a right or wrong or good or bad strategy. In the end, it's how well it fulfills ones goals while meeting ones constraints.