Even competitive intelligence analysts can attend shareholder days
Companies are not fussy about who comes to their shareholder days. All you have to do is ... be a shareholder, which means nothing more than owning a share. A statement of the obvious, but shareholder days are opportunities that are often overlooked. A good competitive intelligence analyst should be attending the shareholder days of target companies, in the role of an inquisitive shareholder rather than for any specific intelligence gathering. Regular attendance of the major companies in an industry will make it likely that you can attend when not engaged in a project about that company, making your visit less likely to fall into an ethical grey area (a grey area that is perhaps a little more white these days when many shareholder days are broadcast live and transcripts easily available).
Attending a shareholder day may well involve no real intelligence gathering, but there is a lot of useful context available from being part of the proceedings. Hearing a CMO speak first hand will make it easier later to understand what you read about them; attending physically will give you a good sense of the company 'vibe', from the meeting rooms used, the employees on duty and the food on offer; and there will be other subtle datapoints on display that you would not find out about by reading reports of the day's proceedings, or even watching it streamed.
This kind of intelligence will come from the informal conversations that take place around the room between employees and shareholders, or around the product demonstrations, and can be very useful additions to a competitive intelligence programme.