First of all, I agree with you and applaud you advocating for sick time off and letting production goals slip to prioritize wellness.

There are reasons people would come to work anyway, and I'm not justifying or excusing or even agreeing with it, just explaining different factors:

• they might not want to admit that they're sick, so if they're able to come in and get through the workday, then they're not sick sick.
• they might be too comfortable in their routines to want to disrupt them for "just a cold" or whatever
• you may not pressure them, but their peers may pressure them
• they might have a strong will to "not let the team down"
• depending on pay structure, maybe using sick time negates what would've been OT, so they make less money even though it's paid sick time
• depending on bonus/raise/promotion metrics, calling out may impact advancement opportunities
• some people define themselves via their occupation, so being sick at home gives them a sort of existential crisis and makes them feel like useless lumps of shit?
• they want to impress a higher up (maybe even you) that they'll sacrifice their own well-being to achieve
• they're fucking morons who learned absolutely nothing from the pandemic that was way too recent to have already been forgotten
• the coffee at work is that damn good
• they hate their family and want to get away
• their family hates them and told them to fuck off and they had nowhere else to go
• if they're able to cash out PTO and/or sick time, maybe that's what they're aiming to do
• they think you're cute and don't want to spend even a single day at home away from your cute face

But in all seriousness (and I know I'm preaching to the choir because you already agree), studies show that productivity is higher when people call out one at a time compared to infecting the whole staff. Don't back down on this issue. You might not be able to send people home when they're sick, but I'm sure you can be direct and say something like:

"Flu season is upon us. I know for a fact that many of us will be getting sick over the next 3 months or so. When (not if) I get sick, I will be using sick time to be at home, resting and getting better and ensuring that I don't spread it to anybody in here. I encourage each and every one of you to do the same. I care more about our health and safety than I do about productivity and goals. I would rather lose you for a day or two than lose half our staff at once for a week. Be self aware and proactive. If I had my way, nobody would even be allowed in the building if they had so much as a case of the sniffles. Take care of us all by taking care of yourself."