In both interpretations of the phrase 'local website hosting' you probably should consider it, yes, but let's just clarify what the 2 interpretations of local may refer to.
Local Website Storage
When we refer to local website hosting, we do not mean that your website will be hosted from a server sat in our Banbury office, running the risk of someone pulling the plug by accident. We use Digital Ocean data centres, from around the world, to best suit you. The World Wide Web is global and therefore so is your website, but it means 'local' in a global sense could be continent or country, and what you should be doing is looking for a local solution, based on your target audience. If your audience is UK based then a data centre in London is local. If you have a European market then you may wish to consider a more central European location, such as Frankfurt or Amsterdam.
We can offer this flexibility, just let us know where your core audience is based.
Local Website Management
If you're interpreting local to mean using a local website company to manage the hosting for you, then we absolutely agree you should look local. Not only does it give you a friendly face but you know you won't be expected to sit in a queue for support questions and will actually have a name to contact.