Why - many reasons - here are the most important ones for me:
1) to block undesired content, such as selected file types
2) to do AV scans on content accessed via web browsers
3) to block access to specific web sites or web site categories
Issues that come to mind
1) with the HTTPS proxy to implement Inspect, you need to add a certificate (from the firewall or your own CA) to web browsers to do the HTTPS content inspections.
2) with HTTPS Inspect, there will be some sites which will not work, and thus will need an added Allow entry to access those sites.
3) with the HTTP & HTTPS proxies - some apps/programs will use TCP port 80 and/or 443, but will not be true HTTP protocol, so you will need to add packet filter policies for access needed by these.
4) with the HTTP proxy, some sites will need a HTTP proxy Exception entry in order to be accessed