You don't need much larger districts to get a much better distribution, depending on how you allocate the remaining seats. Somewhat larger districts would arguably also improve representation for people, on the assumption that if there is a local representative from a party that supports your viewpoints you're more likely to be listened to.
To the first part, while Norway have pretty large districts, the method used to allocate levelling seats to achieve reasonable proportionality (it's not maximally proportional, as there is a lower threshold of 4% to be eligible for levelling seats) maintains a regional link by sorting the parties in descending order of wasted votes (votes that failed to get them a direct mandate) nationally. Then you pick the party with the most wasted votes, then you pick the district with a free levelling seats where that party had the most "unused" wasted votes, and allocate it. You then remove the requisite number of wasted votes, and repeat the process until all the levelling seats are allocated. This means the representatives are all drawn from the regional lists, and are the closest possible match.
The higher the ratio of direct mandates to levelling seats are, the more likely the levelling seats will go to a party that matches the preferences of the population of that region, but even with one mandate and one levelling seat, most places will elect someone via the direct mandate that is withing normal expectations, and so will rarely be any worse off.
Another lesson to draw from Norway is that part of the problem of the US and UK systems is that the local link largely matters because of confusing political and largely apolitical local matters. In Norway, a lot of the issues people in the UK at least write to their MPs about are things you in Norway would write to the County Governor about (there are only 10 of them, for a population of 5m, scale accordingly). The role of County Governor is one often given to former politicians (e.g. about half of the current ones are former cabinet ministers, almost all are former MPs), who knows the system and have connections to get things done, but it's not party political, and they have a civil service staff to assist. When I moved to the UK the notion that writing to an MP was a thing was bizarre - it felt to me like an abject failure of government if you have to write to the legislative about non-political local stuff. You can certainly talk to them in Norway to. When I highschool I just called up parliament for a school project to talk to an MP for my region. But it feels like there is much less need to do so, because you have other avenues and if it's a political issue, the proportionality means it's more likely there's an MP advocating for your view already.
To the first part, while Norway have pretty large districts, the method used to allocate levelling seats to achieve reasonable proportionality (it's not maximally proportional, as there is a lower threshold of 4% to be eligible for levelling seats) maintains a regional link by sorting the parties in descending order of wasted votes (votes that failed to get them a direct mandate) nationally. Then you pick the party with the most wasted votes, then you pick the district with a free levelling seats where that party had the most "unused" wasted votes, and allocate it. You then remove the requisite number of wasted votes, and repeat the process until all the levelling seats are allocated. This means the representatives are all drawn from the regional lists, and are the closest possible match.
The higher the ratio of direct mandates to levelling seats are, the more likely the levelling seats will go to a party that matches the preferences of the population of that region, but even with one mandate and one levelling seat, most places will elect someone via the direct mandate that is withing normal expectations, and so will rarely be any worse off.
Another lesson to draw from Norway is that part of the problem of the US and UK systems is that the local link largely matters because of confusing political and largely apolitical local matters. In Norway, a lot of the issues people in the UK at least write to their MPs about are things you in Norway would write to the County Governor about (there are only 10 of them, for a population of 5m, scale accordingly). The role of County Governor is one often given to former politicians (e.g. about half of the current ones are former cabinet ministers, almost all are former MPs), who knows the system and have connections to get things done, but it's not party political, and they have a civil service staff to assist. When I moved to the UK the notion that writing to an MP was a thing was bizarre - it felt to me like an abject failure of government if you have to write to the legislative about non-political local stuff. You can certainly talk to them in Norway to. When I highschool I just called up parliament for a school project to talk to an MP for my region. But it feels like there is much less need to do so, because you have other avenues and if it's a political issue, the proportionality means it's more likely there's an MP advocating for your view already.