Sure, there are lots out there that are pure analog. The Konus Audio Integrale 2000 is a particularly nice all-analog integrated option in that budget.
Purely analog pre or intergrated amps
Do they even exist any more? I'm looking to eventually replace my current Emotiva preamp and power amp. I'm still on the fence on whether I'm gone to replace them with separates or an integrated amp.
When searching online for something in my desired price range (below $2000 each for separates or <$4000 for an integrated), it seem just about all of them feature built in DACs and/or streamers. The only manufacturer that seems to make purely analog amps these days is Rogue Audio.
Please note, I'm not implying that digital amps are a deal breaker, but it's just features I don't need, since I already have a streamer and am planning on buying a DAC in the future.