Unless you are spending significant resources otherwise, concentration saves are difficult enough for something that is caused with every hit taken, no matter how small the hit is. That's caused by the minimum 10 save dc and by most casters not being proficient in them. It's not like you're sacrificing anything by attacking the wizard more - you just get to stop his spells as a free bonus on the path to killing him.
That depends very much on playstyle and how the wizard is constructed. As mentioned previously, wizards have a ton of defensive spells, but the biggest vulnerability of a single-class wizard is of course AC. In some circles it's popular to start wizards off with a single level of Fighter (for heavy armor, Defense style, and Con save proficiency) or Life/Tempest Cleric (for Bless access, full spell slots, and heavy armor). An AC 21 wizard with Shield for AC 26 is nontrivial to damage in the first place, and if he's got Con save proficiency on top, plus possible Bless/Bardic Inspiration/Paladin aura on top, he is in little danger of losing concentration.
Also, Abjuror wizards don't make concentration saves until you eat through the Arcane Ward.
I haven't seen a lot of Fighter 1/Wizard X at my table (I did make one for my OotA platonic test party but that's about it). However, I have seen plenty of bards and wizards who are reasonably difficulty to damage (AC 16 + Shield) and have decent Con saves (+3 = 70% chance of success on Con saves), which combined with my style as a DM (roleplaying the monsters' goals, not metagaming with DM knowledge about PCs) may explain why I have yet to see very many failed concentration checks.
It's possible that the PCs' choice of spells may have something to do with it too. When concentration spells get deployed by anyone other than the paladin tank, they're usually fighter-enders like Hypnotic Pattern and Wall of Force, and then the spellcaster does go and hide behind a wall or something equivalent to be safe. (Sending an earth elemental to attack the PCs sounds like the kind of thing I dream about in my tactical dreams, but usually consider unfair or unrealistic in actual play. The worst, most unfair thing I've ever done is sic ten Mage Armored Invisible Stalkers on my 11th level PCs while they were resting and partially unarmored (shields doffed, etc.). If I did that kind of thing frequently I would feel like a jerk.)