Hi!
Dedicated server hosting is costly and it has a big resource. If your site does not want very big resources or third party applications to manage, you are probably not a candidate for dedicated hosting.
There aren’t really any disadvantages that you can directly apply to dedicated server hosting, The only factor nearest to a disadvantage that you could apply to dedicated server hosting is the cost of it; this is because dedicated servers cost quite a lot, compared to lower range hosting packages such as shared hosting packages an VPS hosting packages; the cost is only high because the server physically exists.
Setting up your important website on top quality dedicated servers would mean a long term cost-effective professional online environment for your very important business website. But this also fact that people don't understand this simple thing and usually opt alternatives.