Firstly, any negotiation takes years to sign and ratify, so the idea that the UK would be more nimble would make little (if no) difference.
Nimble not just in time but also in coverage, eg not having to satisfy protectionist French farmers for example.
Secondly, assuming that the UK would be able to be more nimble in a negotiation, would this be a good thing? The EU offers protection to its members, and the plurality and combined power means that the EU will get more favourable deals than a single EU (or ex-EU) state would be able to get. Thus, the UK would have to make more concessions to get these deals, especially with more powerful states (US, Japan, China, Brazil etc.) which would have to make up for the additional cost that would be incurred with being able to trade less easily with the EU.
That assumes the UK is in a worse position to negotiate with a third country than the EU, but that's not always going to be the case. Plurality is a bar to getting the deal in the first place.
Also, nimble to do what? To me, that suggests making more trade-offs. These trade-offs that may not well be in the interests of most people. A possible trade deal with the US would have to include some form of relaxing our food standards in order to allow their agricultural products in. This is before we have made significant trade-offs in the pharmaceutical sector, thus ensuring the NHS is in a worse position than it already is. The US loves to insert some very nasty little clauses into trade agreements which effectively mean that UK sovereignty is challenged by large US multinational corporations. Clauses such as "any legislation that may harm the profitability of..." are particularly vicious. The US doesn't just sting smaller states with this kind of thing, it also does it to large states (Australia springs to mind).
Whether the trade offs make the deal acceptable will depend on the merits of each case, but it will be British politicians who decide whether we agree, based the UK's interests, rather than EU politicians, who will have all sorts of competing and conflicting interests to balance, because of the large number of states (and getting larger. Who knows who will join in the next 40 years, it the EU survives that long)
Famed Remainers David Davis and Dominic Raaaaaaaaaaaaaaaaaab as Brexit Secretaries. Then there's pro-immigration Nigel Farage who famously stayed very quiet throughout thie process. To pretend that ending freedom of movement was not one of the biggest things that the majority of leave voters wanted is incorrect.