The testudo formation was never used in pitched battles, it was a tight formation designed for use next to enemy walls during a siege. The strength of the testudo was that the interlocking shields spread out the weight of anything dropped on the formation, such as rocks or pottery. Going into testudo didn't offer much more protection against arrows than simply raising your shield above your head in standard formation, which was always done during a pitched battle in both the ancient and medieval periods. Another thing to consider is that medieval shields weren't uniform, shaped right, or big enough for testudo to be used.

In short, the testudo couldn't be used by medieval armies, and even if it could it wouldn't serve much of a purpose in most contexts.

/u/novashadow1324 has largely answered your question. I would add (and /u/MI13 can tell you far better than I) that the longbow was far from a miracle weapon which instantly rendered heavy infantry obsolete. To think that it did requires you to only fixate on three battles (and interpret them very generously) while ignoring the other occasions when French heavy infantry closed with and butchered unsupported English archers, along with the mountain of evidence indicating that armor could provide quite good protection from them. The longbow was one (rather popular and useful) tool in the English arsenal, not a wonder weapon; there is a reason that every English army to take the field during the Hundred Years War included a contingent of men-at-arms and/or infantry in addition to the archers. Its reputation has been greatly overstated as part of a national mythology.