The previous responders have all made valid points - php is an inefficient way to upload large files, and the load on the servers of multiple users doing this at the same time could well bring a shared server to it's knees. There is a reason DH has set default limits in the way that they have.
That said, Yes, you can install your own configuration of PHP, and set it to allow uploading of "larger" files, though you will still have to deal with the realities of being on a shared server and the finite resources of CPU and memory.
This is not for the "faint of heart", and DH will not help you sort it if you bork it, but will police you aggressively if your CPU and memory usage become inappropriate for a shared server. DH allow you lots of flexibility and give you plenty of "rope" - certainly more than enough with which to "hang yourself"!