In Australia we use Eventor as a central database (which handles membership and event entry, as well as having event-locator tools similar to the British ones). It's not the most user-friendly system around and it was something of a learning curve, but it seems to be well-accepted now and is definitely a big plus for organisers.
Perhaps the main barrier is the cost. We pay 200,000 SEK (about US$25K, I think) per year for the license, although there are a number of license tiers depending on usage and I think OUSA would fall into one of the lower tiers, at least initially. As I understand it, OUSA is not exactly flush with money, so you'd probably need to get your clubs wanting to use it as a shared resource (and be willing to contribute money to make it happen).
In Australia we also required quite a few specific customisations, many of them to do with our membership structure, which is different to the Swedish one (in Australia, clubs are affiliated to state bodies, not directly to the national one, and a member's "primary" affiliation is with their state association). Since you've only got two levels of organisation (national and club), which is closer to the Swedish model, you'd probably require fewer customisations.
I think Eventor is a great tool for national and local event calendar, registration, and results. Especially since it already exists. I recall that OUSA was going to look into the cost and it seems certainly worth considering.
I'll also put on my (biased) work hat and mention that Salesforce can also handle all those database needs, either natively or with some development. The basic CRM stuff like donation tracking and memberships comes essentially out-of-the-box and can be customized easily, and all of the other stuff can be built or integrated (Salesforce is a flexible and pretty easy to develop on PaaS). SF is not cheap normally but for a non-profit the first 10 licenses are free (instead of $150/person/month) and additional ones, if you need them, deeply discounted. It's easy to set up customer-facing sites with access to particular data, or expose event calendar data via an API to build a nice national calendar on a different platform (for instance).
I don't know enough about OUSA's current CRM situation to know whether it is worth switching. I also don't know whether it would make sense to build a home grown solution on SF for all the other needs. Or to build one anywhere. I just know that it's possible and, with the free licenses, a potentially attractive solution.