There will be no practical difference in throughput if you have an additional Core-Switch or not. But it really seems that it is not needed here for functionality. The only problem could be connectivity of the firewall to the switches. With three floors you need a lot of SFP-ports on the firewall to directly connect the access-switches. Or do you have copper from the firewall placement to the access-switches? Firewall-redundancy is definitely more important, if you use Meraki MX, you only need an additional appliance and no additional license. That comes pretty cheap.
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