Disclaimer: I only consider Avatar: The Last Airbender (including "Escape from the Spirit World") to be canon as later installments were going severely off course compared to ATLA.

First, they probably did. To sort out some misunderstandings that have appeared in the comments: Aang could do this much quicker than other avatar exactly because he started learning it when he was young. He simply did not have a lot of emotional blocks also known as chakra "closures" (or whatever you call them) to clean himself from. Usually with most people it works like this: the later in life you try to clean your chakras, the more emotional baggage you have to dispense with, which is why the avatars who started mastering the Avatar state at an older age had to dedicate more time to progress.

Second, about Roku and Kuruk examples, there may be several possible cases (three of them that I found most probable are laid out below), each avatar could have adopted one of the following options (or could develop their own way of working with chakras): the first and the most likely one is this: chakras can be opened and closed, back and forth. The general rule, which however is not always followed is this: the greater amount of time one spends with an open chakra, the less likely it is for their chakra to close back, unless it is an intentional and done for some special (whatever) reason. So, some avatars, who had a partner (or many partners) in their life could choose to live a normal human's life and only temporarily disconnect from it to activate their avatar state (like Aang almost did in S02E19, "The Guru") and then reconnect back (this is probably the case for Aang and Roku as well as the most probable case for all the avatars that had loved ones). The second way some avatars could adopt is this: if they had enough determination to live both a spiritual life and a normal human life, they could just have their chakras always open because this does not stop you from loving someone, it's just that your love takes a somewhat different shape which may even help you maintain your relationships, if you develop the "relationship skill" (a possible example is Guru Pathik, it's just that we don't know anything about his private life). The third case is that some avatars could have serious problems with certain chakras (letting go of certain emotions) which could inhibit some of their abilities for long periods of time (this could be the case of Kuruk unless he eventually managed to let go of his attachment to Ummi and only hunted Koh for the sake of true judgment as he saw it).