First the Gracchi weren't some proto-democrats murdered by the ev0l Senators, they were playing fast and loose with the (unwritten) constitution and set the precedent for other like Saturnius to follow, though they did have some good ideas. Just like the rest of the Roman elite they wanted to get to the top and while Sulla or Caseaer used inspired Generalship and an Army to get there the Gracchi used popularism and the mob. Sulla did a lot of good things for the Republic like helping Marius conquer Africa and defeating Mithridates, he also did a lot of bad things like marching on Rome. The Gracchi were no different.
The real problem was the Marian reforms. By opening up the Army to the landless poor Marius enabled the Romans to go conquering thanks to an effectively limitless pool of manpower, but thanks to Senate intransigence they were wholly dependent on booty from campaigns for their pay and their Generals to get them a demob bonus. This set up a very unstable dynamic and made for an Army which was both a.) exceptionally aggressive and b.) more loyal to their Generals than the State.
Add in the monumental ambition of your average Roman Senator (who all had military experience thanks to the cursus honorum) and you have a recipe for disaster.
Having Pompey beat Caesar or simply butterfly Caesar away isn't going to solve the basic issues of powerful armies dependent on their Generals and amoral and ambitious politicians. However to change that you need such a complete change in the political culture and structure that the Republic as Cato knew it would not exist afterwards.
Edit: Re: Pompey he was a novus hominem, a new man and just wanted to be accepted by the Roman elite as one of them. Caesar was a descendent of Venus and didn't care what people he viewed as his inferiors thought of him. For Casaer outside the Julian clan and the Fabii he had no equals in terms of sheer aristocraticness