REF: DataFrame.to_html should call Styler.to_html

[attack68]

The tracker of items needed to do before deprecating DataFrame.to_html().

Blockers

• Acceptance of the jinja2 requirement for HTML output, since Styler requires jinja2.
• Acceptance of removal/hard break of specific kwargs and all formatting keyword args (see below).

Development

• make Styler.to_html as performant or better than DataFrame.to_html (PERF: halve render time in Styler with itertuples #39972) (PERF: make Styler default formatter arguments statics instead of repeated dynamic #40425) (ENH: make Styler compatible with non-unique indexes #41269)
• make Styler functional for all DataFrames (i.e. including non-unique columns, indexes) (ENH: make Styler compatible with non-unique indexes #41269).
• enhance with ability to style indexes/column headers with styles (e.g bold rows) (ENH: Styler.to_html gets bold_headers and caption kwarg #43149)
• enhance .hide_columns with .show_columns alternative (optional) not necessary
• add the sparsify kwargs (ENH: sparse_columns and sparse_index added to Styler.to_html  #41946).
• add render trimming to prevent browser crash on large data (ENH: set render limits on Styler to automatically trim dataframes #41635)
• decide whether to add or drop max_rows / max_cols / min_rows (ENH: max_rows max_cols kw for Styler.to_html + styler.options #42972)
• enhance .hide_columns and .hide_index to have dual function to hide the entire array, or specific items (API: make hide_columns and hide_index have a consistent signature and function in Styler #41266 DEPR REF: hide(axis=..) replaces hide_index and hide_columns #43771)
• make styler reactive to separate sparse columns and index separately (ENH: add styler option context for sparsification of columns and index separately #41512)
• add pandas options for styler for default output manipulation, using _repr_html_ methods (Opinion requested: Pandas Options for Styler #41395)
• add the ability to render a a table_id even if exclude_styles is True (for back compat)
• add the ability to hide index names ENH: kw names to Styler.hide_index #43346
• add the class="dataframe" attribute by default for google colab (using DataFrame.style loses all default table styling googlecolab/colabtools#1687)

Treatment of Keyword Args

Old Keyword	New Keyword	Reason
buf	buf
encoding	encoding
table_id	table_uuid
classes	table_attributes	extended utility
sparsify	sparse_index sparse_columns	more control of individual components
max_rows min_rows max_cols	max_rows max_columns	min_rows removed since it is console related
bold_rows	bold_headers	included to allows some back compatability
...	doctype_html	adds ability to form a full HTML document or just style and table HTML elements.
...	exclude_styles	adds ability to more closely replicate DataFrame.to_html by dropping extra features.
...	caption	adds ability to set a caption on Styler from the calling method.
na_rep formatters float_format decimal escape	removed	replaced by Styler.format(...) which has more control
columns header index	removed	replaced by Styler.hide_index(...) and Styler.hide_columns(...)
border	removed	deprecated HTML should be controlled with CSS
col_space	removed	should be controlled with CSS, e.g. 'min-width: 100px;'
render_links	removed	not useful. only renders links identified as http[...], not as sub part of string, i.e. other http[...] text. if required should be added to Styler.format(...)
notebook	removed	This seems to only provide minor alignment changes that should be controlled with other CSS
show_dimensions	removed	This information is not needed in an HTML table of the DataFrame. df.shape provides the necessary workaround, and as a last resort caption=f"dimension: {df.shape}" displays the info.
justify	removed	since this is a styling arg which should be dealt with by other methods.
index_names	removed	assumed index names are removed from DataFrame if unwanted. As an alternative hide_columns could introduce a keyword argument to specifically hide the index names row.

[rhshadrach]

@attack68 - from #44451 it appears that you and @jorisvandenbossche are in favor of keeping DataFrame.to_html as a wrapper around Styler.to_html. I'm +1 here as well. I've retitled this issue to reflect that and removed the deprecation tag, but please adjust if this is not correct.