I'll write my solution here in case anyone else encounters this problem:
After André's and mketech's answers, I tried using the -d parameter that I had forgotten, and I found that I could ping other hosts with 8000 bytes, but not with 8972 bytes.
After some testing, I discovered that increasing the MTU on the switch side solved the problem. I have 9000 MTU set in VMware and 9216 bytes on the switch side.
I still don't fully understand the root cause. Traffic is not tagged, and the only feature enabled is LACP.