Talking lagers here. 1L starter wouldn't cut it IME. Also talking about negative aspects of unhealthy, stressed yeast and their contributions to the beer.
Yes, a 1L starter will cut it if grown correctly and pitched at the correct time.
In my humble opinion, stir plates are the brewing snake oil of the twenty-first century. They were introduced to brewing by scientists involved in suspension cell culture (primarily cancer research). Clumping is a problem in suspension cell culture. The purpose of using a stir plate in cell culture is to prevent clumping. It does not aerate as home brewers have been led to believe, especially when the media in the stirred vessel consumes more than 1/3rd of the internal volume.
Here's a test that you can run if you do not believe me. Prepare 1L of 1.040 (10%) wort like you would when making a stirred starter (use extra light DME). Chill and pour the media into a sanitized 1-gallon jug using a sanitized funnel if necessary (alternatively, you can pour the media into a sanitized 1-gallon jug hot and let it cool, but you will need to warm the jug first to prevent stress fractures). After the media has been cooled and transferred to the jug, remove the cap from the White Labs vial, take a cotton swab that has been soaked with 91% isopropyl alcohol, and lightly wipe the surface of the lip of the vial over which the culture will be poured (try to avoid having alcohol run down the sides of the vial). After waiting about thirty seconds, take a lighter and quickly pass the pouring lip through the flame (alternatively, move the lighter instead of the vial). You will need to make quick passes in order to avoid melting the vial. Now, quickly pour the yeast culture into the jug after flaming the lip of the vial, and screw on a sanitized plastic 1-gallon jug replacement cap (most home brewing supply store sell these caps). Do not use a paper lined cap. After the cap has been screwed on, shake the jug until the media is almost all foam. All you need to do from this point forward is loosen the cap after the foam settles down and wait until high krausen, which should occur within 12 to 18 hours (often sooner). Pitch the entire contents of the jug after high krausen has been reached using the same basic aseptic transfer technique that was performed with the White Labs vial (i.e., wipe and flame the lip of the jug before pitching its contents). You will need to ensure that your wort is well aerated.
I guarantee that a 1L starter grown this way will fully attenuate a 5-gallon batch of lager at lager fermentation temperatures without producing off-flavors (a 2L starter will reduce O2 requirements and the exponential phase slightly). In fact, I guarantee that is works as well, if not better than a much larger volume starter that is grown on a stir plate the way that most home brewers make starters on a stir plate. Unlike a stirred starter, a shaken starter that is pitched at high krausen does not taste, nor does it smell foul; hence, there is no need to decant other than the desire to avoid diluting one's wort. The reason why a stirred starter smells so bad is that stirring fast enough to get any kind of gas exchange stresses the heck out of the cells. Yeast produced odors and off-flavors are almost always a sign of stress.