I don't think it would cost close to £700m and I imagine they would renovate the existing lower tiers at the same time to increase the amount of corporate seats there. However I agree with you that it makes zero fiscal sense.
Even building an entirely new stadium would make no commercial sense. Even if we found a commercial partner willing to pay a huge figure of say £25m per season, along with an ambitious increase in match day revenue of £20m per annum, the interest on the borrowing would out-way the revenue increase.
I still believe Spurs fans are in for a shock for this exact reason. Their match day revenue will increase by £50m which will be fantastic, but this will be almost wholly swallowed by interest payments. Therefore the only real benefit will be in their commercial opportunities. These have been hugely bigged up by the board, but they still haven't found a stadium naming rights partner as they're looking for a figure that isn't and I believe they'll struggle to get more than £10-15m per annum for this.
I think they believe the difference in non-broadcasting revenue between themselves and Arsenal of exactly £100m will be instantly bridged by this move, ignoring the difference between the clubs in terms of historic success and prestige. My view is this is fantasy and you only have to look at their revenue in comparison to Liverpool's for a better example of how a stadium isn't a commercial golden ticket. Liverpool have a somewhat small and old stadium, but still have a great commercial revenue of £139m, compared to Spurs £72m.
Their match day revenue will bring Spurs up to Liverpool in terms of total revenue, but at a cost of a huge interest bill which will mean the money available for salaries and transfers will still be dwarfed by the likes of Arsenal, Chelsea & Liverpool (let alone the Manchester clubs).