This is very subjective to the type of the product and the audience who use it. If we talk about a product which is for CRM and the whole purpose is to find a customer using a search and then on one screen show, the details of the customer in any developer made UI. Here, the purpose is to just fetch and display customer details when the CRM professional logs in.
The users here are CRM representatives and the task they do is the same throughout the day. For this, it does not matter how good or bad UX is as the product is serving the business.
Now, let’s talk about other products like Adobe suite, MS Office, Google Products, Mobile Apps and more. Here they are used by a different set of audience and the design is the first step before even anyone talks about technology. User research takes the front seat, many studies revolving around user will happen, design thinking happens and later things are moved as per design strategy.
Here if UX fails then the product fails. There are many big companies who failed by doing such mistakes.
So, UX plays a vital role in the success of any product. Adding to this is one more example: Say you got to know about an e-commerce site which sells some unique stuff. You visit the site, and you are stunned by the look of it and also felt nice when browsing and interacting. Now you have made a choice to purchase from that store and you did it with ease. Till this stage, your experience with the site has been good but later when you received the product you started cursing the site.
The reason is you might have got late delivery, worst packaging, damaged piece, no refund policy etc. Even after the design of the site has given you the best experience to buy, your overall shopping experience is worst. This means a product success depends not just on design but also many other factors which all combined is User Experience and not just design.