Along the row players generally take advantage of the alternate notes when they like. It isn't as though there is somebody standing ready to whack them with a ruler if they deviate from the general pattern. Beginners may limit themselves more, but as they progress, they branch out and experiment to find new possibilities, just like the cross rowers do. Along the row playing lends itself to an older more bouncy style, similar to the difference between C#/D and B/C accordion players. Some types of tunes benefit from this , others don't, but just as a Cross Row player can adjust their fingering or bellows work to get more of that effect should they wish it, Along the rows Players can do the opposite if they feel the need.
What do you mean by across rows style? Is that hard?
I don't understand why anyone does not cross the rows. It gives you several options for runs of notes and for harmonies. And you don't need to change your hand position as often.
There are real differences in the general sound of the two different methods ( and there are different versions of both ) so it is a good plan to start out in the style that is used by really good players you like to listen to, but I don't see either way of playing in the long run as being much more limited than the instrument itself.
A lot of people start out in the along the rows pattern because it seems how the instrument is organized, where cross row fingering isn't at all obvious, and generally requires some initial instruction at least to get anywhere at all. Having a good teacher right from day one is the best way to go for either style. It is too easy to paint yourself into a corner with bad habits otherwise.
Dana (a cross rower who occasionally plays along the rows if it suits the tune better )