There's a reason virtually every culture developed hand-held shields for close-combat and why they continued to be used literally for thousands of years. They were very effective. In 15th century Europe, it was only the combination of the development of full plate armor and two-handed swords combined with heavy pole-arms and powerful missile weapons that finally reduced the long reigning value of the shield in warfare. The Medieval style of sword and shield fighting is distinctly different from the two-hand grip and quick full-arm slashing cuts of Kenjutsu. Medieval short swords are properly wielded with more of a throw of the arm and a twist of the hips while making passing steps forward or back. Strikes are thrown from behind the shield while it simultaneously guards, feints, deflects, or presses. A sword and shield is a great asset over a single sword alone. Fighting with sword and shield offers a well-rounded and strong defense that safely permits a wide range of both direct and combination attacks.
A sword can cut quite well from almost all angles around or underneath a shield. Indeed, since the shield side is so well guarded, the opponent is the one limited to attacking to only one side ?the non-shield side. While a large shield does indeed close off a tremendous amount of targets to an attacker, it also limits, to a far smaller degree, freedom to attack by the shield user. As it comes out from behind their shield to strike, an attacker's weapon can be counter-timed and counter-cut ?and this is indeed one tactic to employ against a shield user. Yet a shield user's attacks are not at all one sided. A shield can be used offensively in a number of ways and at very close range.
Katanas are powerful swords used with strong techniques, but thinking they could simply cleave through a stout Medieval shield is absurd. Even with a katana a shield cannot simply be sliced through. Medieval shields were fairly thick wood covered in leather and usually trimmed in metal. Not only that, they were highly maneuverable, making solid, shearing blows difficult. More likely, a blade would be momentarily stuck in the rim if it struck too forcefully. Unlike what is seen in the movies, or described in heroic literature, chopping into a shield's edge can temporarily cause the sword blade to wedge into the shield for just an instant and thereby be delayed in recovering or renewing an attack (and exposing the attacker's arms to a counter-cut). Shields without metal rims were even favored for this very reason.
Kenjutsu (Japanese swordsmanship), though consisting of very effective counter-cutting actions, also has no real indigenous provisions for fighting shields. Although a skilled warrior could certainly improvise some, those unfamiliar with the formidable effectiveness and versatility of a sword and shield combination will have a hard time. The shield was not used the way typically shown in movies, video games, stage-combat, or historical role-playing organizations such as the SCA. Fighting against a Medieval shield is not simply a matter of maneuvering around it or aiming blows elsewhere. If a warrior does not really know the shield, or hasn't faced a good shield fighter, then they cannot be expected to know how to ideally fight against it.