Part of the problem here is in roster fit. Randall Grichuk doesn't really fulfill a need. He does hit lefties well, but looking at his profile he does nothing that Seiya Suzuki will (probably) be asked to do. For example, Grichuk has been a pretty bad center fielder as of late - and as he hits his mid-30's, this feels like it checks out more and more. He's a -16 DRS over his last 1600 innings in CF. So he's mostly confined to RF and LF - which Suzuki could play. As well, he's been pretty bad against RHP most years. Yes, he did have a 115 wRC+ last year, but this feels like an outlier. His SLG was way up against RHP . years prior he had wRC+ of 88 (2023), 62 (2022), and an 82 (2021).
Justin Turner does something the Cubs dont have - they don't have anyone who hits right handed and plays 1b. You could say Tucker could swing into 1b (he's had nominal playing time there since 2019) and he's good against LHP, but for pitchers who have splits, it's sometimes good to have the RHH 1b option as well. Turner's old, and we shouldn't count on him to be amazing, but he's off a season with a 117 wRC+ and while you can argue Grichuk is better against LHP very effectively, Turner is likely going to have more opportunity and is a better roster fit because he's still more than capable against RHP. Grichuk will probably be a pumpkin there. Turner also has little competition as a RHH 1b - there isn't even a prospect that fulfills that role. Kevin Alcantara or Alexander Canario (though I have reservations on both for different reasons) could realistically be a RHH OF'er sometime during 2025 - the Cubs don't have that at 1b outside of maybe popup prospect Johnny Long. Owen Caissie hits LHH and would probably need some RHH protection at the very least.
In that regards, we should look at fWAR in less of a pedantic way. Since fWAR is a cumulative statistic, one in which usage matters, the Cubs probably have more use for Turner. Turner can play DH and 1b, and will play more, giving him more of ability to accrue fWAR with the Cubs. It may be that Grichuk ends up posting better WAR numbers, but how the Arizona Diamondbacks can find time for him will differ from the Cubs and with bench players, their usage and utility matters. The Cubs likely believe they will get more milage out of Turner, and while there's risk employing a 40 year old bat-first player, I'm not that disinclined to see their reasoning for a 1b/DH over the corner OF'er.