I don't own one personally, but a couple of lads from my club do. Between doing the nitrox course and CCR course, I dived with nitrox the grand total of one occasion, and the only reason for that was I was using a hired tank that had been filled with nitrox by the previous user, half depleted and was given an air top up.
When I did the nitrox course, somebody asked the instructor if we needed our own analyser. He said we didn't, as normal practice when collecting your fill is to check the fill in the shop and sign to say you've checked the contents, and the blending station will always have an analyser.
The same person often tells a story about a dive outfit in Indonesia, where they don't pay heed to such trivial matters as safety. They were loading the boat and the cylinders, which were filled with EANx 32 were stood on the jetty. One of the dive operator's staff started passing a clipboard around, asking everybody to sign. When it got to him, he asked for the analyser. The dive operator queried why he needed it and he replied, "You've just asked me to sign a piece of paper saying I have analysed and labelled my cylinder - I haven't." . He then told him there was an analyser on the boat and he could do it when they were under way. "Fine! I'll sign it when I've analysed it then!". He then told him the paperwork had to go back to the shop, so he signed it to save any further argument. Once they were under way, he asked for the analyser - they didn't have one!
I was on a liveaboard in Scapa Flow, Orkney (technically part of Scotland, but if a local hears you say so, they get angry and tell you they're Orcadian). Looking at the booking T&Cs, they point out although they have an analyser aboard, it's primarily for their use and is a backup for your own, and they expect to see at least one analyser per group of divers if they want nitrox. On the boat though, when he gave me a 32% mix for my bailout, his first question was "Do you want the analyser?". I suppose the translation of the website statement is "We have an analyser you can use, but if it is wrong, don't blame us!".
You can get away without having your own, but if you use nitrox a lot, the convenience of having one is worthwhile.