Grant did not fight a war of attrition against Lee in Virginia. Grant fought a war of maneuver against Lee, attempting again and again to pass Lee's right and get between him and Richmond. Lee repeatedly countered these maneuvers, turning each one into a bloody confrontation and repulse; but that was not Grant's chief aim. Any look at a map of the Overland Campaign will make it immediately obvious what Grant was trying to do.
The Confederate force was not "qualitatively superior". There is no reasonable standard by which it was better led: there is no military standard by which Grant was not one of the very greatest commanding generals in American history, possibly the greatest.
Ulysses S. Grant gets his high reputation as a general for his accomplishments. He formed the Army of the Tennessee, probably the most successful unit of the entire Civil War. He pioneered combined land-sea operations (with Admiral Andrew Foote) on the Tennessee River. He won important battles at Ft Donelson, Shiloh, and Vicksburg. Vicksburg had been considered impregnable; Grant's victory there, which opened the Mississippi River, was probably the single most decisive military result of the Civil War before Appomattox. His Vicksburg campaign is studied as one of the great pieces of maneuver warfare of all time.
Grant was the architect of the grand strategy that finally ended the Confederacy. He had the Army of the Potomac keep contact with Lee in Virginia, and sent Sherman on a wide flanking maneuver, down thru Atlanta to the sea and then up behind Lee. He also worked well with his political leadership, and grasped the realities of commanding a volunteer army in a republic. He understood the impact that the election year of 1864 could have on the Union's winning the war. This grasp of high strategy, both in theater-wide military operations and in political realities, is one of the most striking differences between Grant and other generals of the era – particularly Lee, who seemed interested only in Virginia.
Grant conducted the Overland Campaign, which strategically looks almost identical to the Vicksburg campaign. He displayed the same tenacity and focus as he displayed at Vicksburg. He displayed his great ingenuity and command of his logistics at Cold Harbor, with a daring and stealthy movement across an engaged front and over the James River. That movement effectively pinned Lee down in Petersburg, and ended the Army of Northern Virginia as a mobile fighting force. The subsequent siege dragged on forever, but the military outcome was no longer in doubt. (The political outcome was still up in the air until Lincoln won reelection; but in pure military terms, the outcome of the siege was inevitable.)
During the Civil War Grant captured 3 entire Confederate armies: at Ft Donelson (12,000 men), Vicksburg (29,000), and Appomatox (28,000). He very nearly had a 4th army at Chattanooga. (No other Civil War general captured any armies.) This is a stunning accomplishment, difficult even to compare with other results. Against that, Grant seems to have made only 3 tactical mistakes over the entire war:
- Not closing his right flank at Ft Donelson, which permitted Forrest's escape, and could have freed the entire garrison.
- Not having his men entrench at Shiloh. Events proved this a mistake; but it should be noted that entrenchment was not yet standard practice. It was still early enough in the war that Union generals thought entrenchment sapped the soldiers' morale.
- The last assault at Cold Harbor (June 3). Grant wrote frankly in his memoirs about his regret in ordering that assault.
Just 3 tactical mistakes in 4 years of extremely active campaigning seems a pretty remarkable record. It's difficult to find a standard to compare it with; but I make more frequent mistakes than that at my own work, and I don't have an enemy actively trying to thwart me.
Grant had a lower casualty rate than Lee (casualties per 100 soldiers) during the Overland Campaign and over the course of the whole war , despite operating continuously on the offensive. I think Grant's casualty rate was at the low end of the range of Civil War generals, but I don't have that table in front of me. I do know that Lee had the highest casualty rate among Civil War generals.
Grant's reputation is due to his accomplishments; if anything his reputation is less than his accomplishments merit. It's not clear that any Civil War force was ever "better led" than the ones led by Grant.
Apart from the mistaken assumptions in the question, it's tough to know what the question is supposed to mean. Obviously a military commander can use attrition tactics, if he has the resources to sustain it and his political leadership condones it. His job is to win: his means are "whatever it takes", subject to the laws of warfare. Is the question "Should he?" That's not readily answerable.