If a child is floundering, then sure a single effective and consistent algorithm is great... Algorithms are best that work for the person. Some algorithms are more effective if someone has a strong working memory others use methods to reduce memory load.
I think it would probably be just fine even for a child who's not floundering. Most of the world's great math thinkers weren't taught with Investigations, anyway, so I don't think it's necessary to do the amount of exploratory work that the curriculum seems to require with basic arithmetic. I also don't think that a personally discovered or picked calculation method is always going to be the best for a particular student, since I don't think that beginning students are so wise as to always pick what will work best (this is why I don't believe in radical unschooling for the masses, either). And while I think it's good to develop fundamental problem-solving meta-skills, I don't see much point in spending a lot of time developing basic number sense and calculation skills this way. A little time, maybe, as fun enrichment, but not a lot of time.
But my feelings on this might be because my son nearly instantly grasped so much of arithmetic, and has never shown any problems learning or remembering procedures like long division either. ETA: Every child is different, and I can see that for many children it's probably appropriate to start developing problem solving skills with the main tools they have available early on-- basic number manipulation. I can see some sense to it.
I have started consistently asking DS to work out how to do some algebra operations on his own before a new skill is introduced, though. I also ask him to do a fair bit of the algebra in his head, to improve his memory and let us go a bit faster. I wish I could actually encourage him to do more in his head, but he needs some practice on doing neatly organized written work too.
