this is true in general but
1) vivado webpack edition (ie free) lets you write (and flash) a bitstream for some of the small chips. i know it at least works for the artix-7 family because i'm doing it every day lately
2) for the artix-7 (and some lattice chips) you supposedly can use OSS (https://github.com/SymbiFlow/prjxray). i haven't tried it yet but one problem i can foresee is that the OSS tools won't infer stuff like brams and dsp. in fact the symbiflow people (i think?) explicitly call this out as the part of the project that's a work in progress.
some useful links:
https://arxiv.org/abs/1903.10407