Having a shield is extremely useful not only defensively, but also offensively. After parrying an attack, the parried enemy will take double damage for a short duration, not long enough for a 3 hit combo with most weapons but a sword or mace secondary attack after a parry will oneshot most enemies and will deal huge damage to minibosses.
Plus early two-handed weapons suck due to low parry ability. Stagbreaker and Iron Sledge can be very useful for their area damage but you might have to tank a few hits while using them.
it starts to change in the Mountains, where a Crystal Battleaxe can parry a wolf (provided it is isn't starred) but it has crappy dps so you are still better off with a 1handed weapon+shield.
2 handing really starts shining in the Plains though. Blackmetal atgeir can parry even Lox. and its secondary can clear Fulings. Just watch out for Berserkers and starred Fulings. Gonna want a shield if you want to parry those.