Basically every entity with turnover exceeding AED 375 000 should either register for VAT or to apply for VAT registration exemption. You can apply for exemption if all transactions are zero rated. For example all customers reside / are established outside UAE (in case customer is individual – he should reside outside Persian Gulf countries). UAE is part of larger VAT system made from Persian Gulf countries, basically it is simplified to EU VAT system.
Since VAT was introduced comparable recently, most free zone entities still do not meet these requirements, i.e. they neither register to VAT, nor apply for VAT registration exemption. Administrative penalty for non compliance with the above is AED 10 000.
It is likely that one day authorities might start paying more attention to this. It might be especially relevant for companies in Free zones which require to submit audited statements (since it is obvious then from turnover, that company did not comply with VAT liabilities, so it is easy to track such companies). Moreover, having a company which does not comply with VAT laws might lead to more issues depending on the case. If such company decide to obtain tax residency
certificate or apply for other official document from authorities they might check that company failed to comply with VAT laws. Basically most of the documents are issued only for companies in good standing from legal perspective, so failing to comply with VAT laws is making the company not in good standing from legal point of view.
Having VAT registration number also helps to build more substance (UAE does not issue TIN, so VAT number creates substitute and might be used as tax ID). Moreover, since in UAE there are no corporate income tax reporting having quarterly VAT returns helps to prove that company derived profit and reported everything properly if this is needed in the future.