Pitching is the one field that it is not uncommon to see substantial increases in production in years 28 - 38.
It is not unusual for a pitcher's command to improve as they enter those years. Someone with above average stuff, but below average command can see their command increase at a higher rate than his stuff decreases.
Also, those are the years where less effective starters are often moved to relief, where their increase in velocity often is a difference maker in middle of the road pitchers.
Finally, as Craig has mentioned, a tiny change in a pitcher's mechanics can cause a much greater change in production, both positively and negatively, than similar changes for a batter. When a young pitcher makes it to the majors, they are mostly convinced that they have star potential, and are reluctant to make changes to the things that they believe caused their previous success. By the time that they reach their middle to late 20s, the smarter ones begin to realize that their performance is more likely to decrease than to increase, unless changes are made. It looks like pitching labs and pitching coaches are starting to convince pitchers at a younger age that change can be dangerous, but it can also be very good.
I think that the Cubs program is beginning to have an impact on older pitchers, many from other organizations, and their much maligned, but successful efforts to build their bullpen "on the cheap" as some have described it, is starting to show very good results. Partly, I believe, this is due to the fact, as many have pointed out, that relievers tend to be the most variable in effectiveness from year to year, making turnover in the bullpen a good thing. But most promising to me is that it looks like it can also produce results from those at a younger age, with earlier and greater results.
At this point in his career, I would hate to see Alzolay turned into a permanent reliever, but it is nice to see that he seems to have substantial potential as a reliever, and I kind of like to see the team go back to the older system, where younger pitchers were usually started off as a long reliever, and gradually worked themself into the starting role as they prove themselves.