Is there a simple Bash tool which can quickly render basic HTML?

lynx has a "dump" mode, which you can use with watch:

$ watch lynx https://www.google.com -dump

From man lynx:

   -dump  dumps  the  formatted  output  of  the default document or those
          specified on  the  command  line  to  standard  output.   Unlike
          interactive mode, all documents are processed.  This can be used
          in the following way:

          lynx -dump http://www.subir.com/lynx.html

          Files specified on the command line are  formatted  as  HTML  if
          their  names  end  with one of the standard web suffixes such as
          “.htm” or “.html”.  Use the -force_html option to  format  files
          whose names do not follow this convention.

This Ask Ubuntu question has many more options.

w3m is another program that has a --dump option.

It is the backend Emacs' most popular web browser.

There are at least two programs named html2text (1) (2) which do this job.