It's not really a 'could' spill over, it definitely would.
A very high proportion of institutional investment is tied up in CRE. If enough defaults happen it might even be worse than 2008.
Doesn't mean we should tip the scales in favor of CRE or the banks, though. If it comes to pass, we should nationalize the assets and socialize retirement (more). If we didn't have all our retirement accounts in private markets our exposure to this kind of error wouldn't be so high.