While I don't like the idea of signing Griezmann, your opinion is too extreme. We wouldn't have won 1999 CL with your line of thinking by not signing Teddy Sheringham.Just like how City saw no issue signing Kovacic who is injury prone himself. Akanji was signed when he was 27. Kyle Walker was signed when he was 27.
Let's say Giroud would have been open to move to us when he left Arsenal and Chelsea, when we need an experienced CF like we do now; you would rather keep your hands in the pocket writing off a few seasons to develop Hojlund? Only to see Giroud to maintain a high level of performance for half a decade. We saw for ourselves recently that signing right age profile prospect doesn't mean jackshit because bad luck may render players into crock Pogba, Bailly, Martial, or they're just not good enough van de Beek, or off the pitch issue can take away players like Greenwood, Sancho.
Successful teams will try to get healthy portion of recruitment consisted of younger age profile, but there is no ridiculous extreme policy like you suggest. Long term also built on short term luck and good planning. Man City wanted Kane 2 seasons ago when he was 28 already. They're in luck of getting Haaland, but for them to be lucky, plenty other clubs remain unlucky. Arsenal Chelsea Real Madrid all can do with a better CF. Bayern signed Kane for their club record fee.