My recommendation to always have pull-up for EN may be ill-advised or even misleading, but, still, understanding the danger of receiving more downvotes, I am taking a risk to ask the question in the body of my answer. It is done not because of the lack of respect for SE policy that discourages asking questions in answers, but only to keep the track of the OP question context.
What confuses me is the persistence (for a few years) of incorrect (?) description of EN/EN_N pin functions in the TI datasheet for the case of external control operation: If controlled externally, must be held low at least for 50 ms after VDD has reached its valid voltage level, for both EN and EN_N pins. Can someone confirm (or disprove) that this is in error and that for TUSB320HA (EN pin) it must read must be held HIGH at least for 50 ms?
I understand that the OP question is about the enable signal controlled internally, but the seeming "asymmetry" of device initialization signals makes arguing via example circuits for TUSB320LA (as only these are given in the datasheet) at least insufficient.
My original (most probably, incorrect) answer, edited into the conditional mood:
See the table in the datasheet, page 3, section 5 Pin Configuration and Functions. The descriptions for rows EN_N/EN read:
EN_N Enable signal; active low. Pulled up to VDD internally to disable the TUSB320L device. If controlled externally, must be held low at least for 50 ms after VDD has reached its valid voltage level.
EN Enable signal; active high. Pulled down to GND internally to disable the TUSB320H device. If controlled externally, must be held low at least for 50 ms after VDD has reached its valid voltage level.
One can infer from these descriptions that the devices, when controlled internally, carry out the same initialization operations, and in the active high device certain "internal" enable must be held low for at least 50 ms. If this is the case, and if the EN signal is not buffered, shorting the EN pin to 1.8/3.3V may prevent the device from performing the initialization operation.
In this case, external control of the EN pin is not implemented and therefore the EN pin is tied to 1.8 V or 3.3 V.– V.V.T Oct 05 '22 at 07:10...must be held low at least for 50 ms ...which is probably a typo (must be held high?). Have you had a hands-on experience with a design for TUSB320HA application, where pin EN is tied to 1.8/3.3V? – V.V.T Oct 05 '22 at 15:51Another answer pointed out that part of the datasheet says, "...external control of the EN pin is not implemented and therefore the EN pin is tied to 1.8 V or 3.3 V," the key word being "tied", so it seems OK to omit a pull-up resistor.
– ide Oct 05 '22 at 17:46