Those dates are misleading. For example, I’m still on an Athlon II X2 270 that I bought in 2012 (released 2Q 2011 according to CPU-World) and I don’t see sse4_1 in my /proc/cpuinfo flags, let alone anything AVX-related.
For reference, here’s what the Athlon II X2 270 does support:
fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm 3dnowext 3dnow constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid pni monitor cx16 popcnt lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt hw_pstate vmmcall npt lbrv svm_lock nrip_save
…and yes, that is a dual-core CPU but, for my puttering around for various uses (diagramming, pose/perspective references, plans to do some model making for simple 3D games and some video editing, etc.), Blender currently works perfectly well on it.
(My budget’s mostly been going into more and bigger hard drives and, given its relatively small size, I was hoping to at least keep this machine ticking along until the projected opening of the new chip fabs in 2024 or 2025.)