If I use a module with "Custom HTML", I can customize the page, but always the original page (with box & counter).
Why not provide the ability to create the whole page without having to modify PHP or CSS. For example using the Joomla editor (or JCE) where we can use the shortcodes related to the already installed plugins.
because "creating custom page" in Joomla means for everyone something else. Someone is usin Joomla articles, someone some page builder, someone K2, ZOO or any other component. Moreover, Coming soon page can be activated regardless used template. Using just some Joomla article or whatever else, will not solve styling of custom Coming Soon page, there are no tools for that, so the coming soon page will be dependant on template CSS, which, when not ready yet (and that is the point of coming soon), will look "somehow". FInally you will find that you will need to modify CSS and PHP again, directly in your template.
Anyway, as Custom HTML file gives you complete freedom, you can for example crate you coming soon page using your favourite WYSIWYG editor, Joomla editor, some Joomla page builder or wahtever else, then save it as html, and simply use that saved html file as your coming soon page.
Shortocdes could be used even in your custom html using JHtml::_('content.prepare', $text) function. Also any other Joomla functionality could be used.