The simple answer to this question is, “yes.” Every limited liability company should have an operating agreement. Just because a Texas LLC only has one member and owner does not mean that this document does not serve any purpose. In fact, it is just as important as it is for companies with multiple members.
One of the most important reasons for a single member LLC to have an operating agreement is to definitively create a separation between the individual and the company. An attractive component to this type of entity is the limitation of liability and the tax structure. This document helps create the separation needed for any potential liability issues and for taxing authorities. The more defined and documented the separation is, the better off the individual will be if something goes wrong.
The operating agreement can outline what happens when the owner dies or can no longer run the business for some reason. It can include a succession plan in order to maintain the continuity of the business under these circumstances. It can also show how money flows into and out of the company and helps the owner avoid falling under Texas default rules when it comes to LLCs.
There may also be other, more specific reasons for a single member LLC having an operating agreement. The more defined and clear the agreement is, the more protection it may give to both the business and the member/owner. It would be wise to work with an attorney to identify all the issues that need to be addressed in it and to create it.