37 is not too old for McKinsey. The more important question is whether joining as an Associate gives you enough additional value relative to the experience you already have.
With a PhD and around 10 years in biotech, your industry experience can absolutely be useful, particularly if you work in life sciences. But you should not assume that previous seniority will automatically translate into faster promotion. Once you join, progression will largely depend on how you perform within the firm's system.
I would get very specific about what you expect McKinsey to unlock. What roles could you realistically access after 2 to 3 years there that you probably could not access today? You can read this guide on changing careers into consulting around age 40 if you're trying to evaluate whether the experience and brand justify the career reset.
The lifestyle question matters just as much. The issue is not whether a 37-year-old can handle consulting. It is whether the hours, travel, and reduced control over your calendar are worth the outcome you want. If McKinsey fills a specific gap in your career, the move can make sense. If the main attraction is prestige, I would think much harder about the tradeoff.