Well in most cases stiff mast is a good mast, this is one of quality factors. Cheaply built masts are rarely stiff. Stiffness is mostly important for radiolink communication and satellite dishes (form of radiolink in fact) – where power beam is narrow and focused. Imagine a laser pointer that is aimed at a tower clock from outskirts of your city. Not easy to keep it steady pointed directly on the clock face… but fix it to the building and the beam will be glued to the point miles away.
In most countries masts are created to allow max deviation of 1:100 of its height. For 30 meters mast it is max 30 cm at the top! I would not call it a little, that’s couple hundred meters over 10 km. One of the cheapest ways to improve this is to top the mast with separation crown with additional set of guy wires.
Stiff masts are also nicer to service (you simply feel safer on one)