Simple versus exponential
A simple average weights every period equally, so an extreme value affects it identically whether it occurred yesterday or forty days ago — and it drops out abruptly when it leaves the window.
An exponential average decays older values smoothly, which removes that artefact and responds faster to change. For most purposes the exponential version behaves better.
Lag is the feature
Any average of the last N periods is by definition behind the current price. That is what makes it smooth. A shorter window reduces lag and reintroduces the noise the average existed to remove.
There is no setting that gives you smooth and immediate, and searching for one is how people end up with twelve lines on a chart.
Fitting the window to past data makes this worse. Any period can be tuned to look excellent on a chosen history, and the tuned value almost never performs the same afterwards. A parameter selected because it worked last year is a description of last year.
Crossovers and the honest evidence
A fast average crossing a slow one marks a change in recent trend relative to a longer one. Tested as a mechanical rule across markets and periods, results are inconsistent and usually negative after transaction costs.
Widely watched levels can become briefly self-fulfilling because many participants act on them, which is a different phenomenon from predictive power.
What they are good for
Seeing trend direction without squinting through noise, comparing current price to a recent baseline, and defining a consistent context for other measurements.
FBT Swap shows moving averages alongside other readings with their periods stated, as description rather than instruction.