I also know this is EU wide. For instance if she were to get a job in Switzerland I'd be free to get a job over the border in Germany.
That's not entirely correct. I am not sure about this particular scenario (cross-border work residing in Switzerland as the spouse of a Swiss citizen) but it's important to note that you do not have an EU-wide permission to work and reside anywhere, your status is always tied to that of your partner and contingent on both of you effectively living together (what we are talking about is a right for your partner to a family life hence an almost unconditional right for you to join them but no special rights beyond that; your own right to live and work in the EU derives from your partner's).
Remote work would in principle be legal but you cannot easily obtain a work permit and reside in another EU country merely because your spouse resides somewhere in the EU. On top of that, EU freedom of movement rights only apply when EU citizens are in another country than their own. It might or might not be easy for you to move to Switzerland but that depends on Swiss — not EU — law.
But... What if I'm the main earner? Could I apply for a job in Denmark first with the right to work in Europe and then we both move there together?
It's a little more complicated but that ought to be possible. One option is for your spouse to find work in Denmark. That would take care of your residence permit. It doesn't matter what her income is or whether you are the main earner, it only matters that she has work that is “effective and genuine” (part-time or short-term work is OK, minimal wage too).
Failing that, your spouse would need to qualify as an “economically non-active” EU citizen to sponsor your residence permit. She can do that based on your (common) income but relying on savings would probably be easier, certainly for your first application. You will also need to secure health insurance and to ensure the employer is comfortable going along with this.
See US Citizen with EU Spouse who doesn't yet have a job, Moving to Germany with fiancée (both EU citizens) because of work reasons. What if she does not find a job?, and Residence in Germany with an EU spouse - can the non-EU spouse go over first? for more details on how all this works.
And how does this work in the new field of remote working? If we were to stay in the UK would I be able to get a job elsewhere in Europe by right of this marriage or would we have to actually move to EEA/Ch soil?
Neither your spouse's citizenship nor local immigration law would be directly relevant as you are not trying to secure residence or work in the country. The difficulty is navigating employment, tax, and mandatory insurance law that are not always designed to facilitate remote work. As far as I know, employers mostly handle that by using a local (= UK) branch or third-party business to set up payroll for you or offer to hire you as a contractor instead of a bona fide employee. It can be complicated or illegal/too risky in some cases but does not generally depend on your citizenship or right to work in the country where your prospective employer is located.
If the employer has no presence in the UK and is not used to hire people across borders then you might need to move to that specific country. EU law doesn't help so much and working from another EU country might not be enough to alleviate all difficulties. For example, I am aware of several Dutch companies with fully remote employees located inside and outside the EU who won't hire anybody located in France (even French citizens, who obviously have the right to work both in France and the Netherlands).
