Is there any security or operational problems if I do not have any .htaccess file in drupal root? I realise that having the .htaccess file in the root of my installation is probably the way the program is designed to run, but I was having some difficulties accessing the site, and then fixed the problem by deleting the .htaccess file in the root. But then it made me wonder if this was a good idea to leave my Drupal 7 installation without a .htaccess file in the root at all. 

Is there any security or operational problems if I do not have any .htaccess file in drupal root? I imagine that I would have to put it back in order to enable clean URLs.
You may have some problems, depending on how Apache is configured.

People may be able to browse directly to some hidden files.  Look at lines 6 and 73 in the .htaccess to see what it restricts.

People may be able to browse directories directly.  See line 10. 

The site may not work right if you accidentally put a file called index.html in the root.  Line 20 makes index.php the primary file.

Clean URLs won't work.  I am not 100% sure if image cache will, either.

There may be some PHP security issue, but the php_flag directives have been standard settings in php.ini for a several years now.

Are you on shared hosting?  If so, the problem with the .htaccess could be the Options lines.  Some hosts restrict these.  Everything else should be feature checked the the &lt;IfModule&gt; directives.

It is possible to not have a .htaccess in the DOCROOT by placing the contents into the Apache config for the site, or in an include.  On high volume sites, there are some performance gains from doing this (.htaccess is read each request, where Apache config is read once when it starts).