It has a choice. It can choose to accept the EEA and all that comes with it. Or not to.
Is trade with the UK important to the EU? Sure.
Is trade with the UK more important to the EU than trade with the EU is to the UK. Not even remotely.
Even EEA becomes a bit of a minefield for companies due to country of origin rules. For instance you can't get tariff free trade by setting up a trade deal with say the US, importing US goods sans tariff and then selling them on to the EU via the EEA, as the country of origin for those goods is still the US, when a UK company sells those goods on to the EU via an EEA deal it does so under the terms agreed between the EU and the USA.
There are other downsides to joining the EEA in addition to the membership fee and the need to follow EU regulations. While EEA members belong to the Single Market, they are not part of the deeper integration that occurs within the EU. For example, as an EEA member Norway does not belong to the EU’s customs union. This means Norwegian exports must satisfy ‘rules of origin’ requirements to enter the EU duty-free.2
With the growing complexity of global supply chains, verifying a product’s origin has become increasingly costly. If the UK joined the EEA, part of this cost would be borne by UK firms. Exporters would have to limit their use of inputs imported from outside the EU to meet the EU’s rules of origin (Stewart-Brown and Bungay, 2012). The EU can also use antidumping measures to restrict imports from EEA countries, as occurred in 2006 when the EU imposed a 16% tariff on imports of Norwegian salmon. Campos et al (2015) find that Norway’s failure to undertake the deeper integration pursued by EU countries has lowered Norway’s productivity.