Pro: They aren't putting all of their eggs in "one-basket" by investing heavily in one or two guys
Jacob deGrom. Carlos Rodon. David Price. Stephen Strasburg. Patrick Corbin. Robbie Ray. The list goes on and on. The risk of investing so much capital into one top-end starter is possibly the biggest gamble a front office can take, and the one that can do the most damage if it goes poorly.
Injuries can happen to any pitcher at any moment. We like to talk a lot about getting starters who are not "injury prone" but in all honestly, you are holding your breath with 95% of pitchers in this league that they'll avoid any IL stints, let alone missing entire seasons. That hurts no matter who the starter is. But it becomes crippling when you paid that starter $25+ million to produce for your team.
Look at the Tampa Bay Rays. Coming into the season, they had more pitching than they knew what to do with. By the time the trade deadline came around, they were also looking to acquire more starters. Even after the deadline, they've continued to have starters go down with injury. It's never been more true that you cannot have enough pitching.
So for a team that has so many pitching needs, they can't really afford to not bring in multiple options, knowing that injuries will eventually happen. If they do rely on someone like Hudson or Thompson in their rotation, what happens if they have one or two injuries early in the season? Now your rotation has both Thompson and Hudson, plus someone like Liberatore filling in. Things can go downhill quickly.
This is not advocating against going after top-end pitching. I think it's a must for St. Louis. But I do see why they feel the need to add at least three starters, as investing in just 1-2 top-end guys can cripple with one or two untimely injuries.