First, it is inarguable that "fly straight out" is non-standard phraseology and is not specified in a thick FAA manual of full of standard phraseology. The requirement to have a pilot fly straight out does not rise to the level of NEEDING to resort to non-standard plain English phraseology to make the meaning clear since "fly runway heading", a standard phrase, would suffice. So there is no justification there.
Second, since a VFR tower launches into the airspace of either an approach facility or an enroute facility, it does so at the direction and with the permission of that facility and there are precise methods specified for doing this.
If the airspace into which the IFR flight is being launched is radar controlled AND the aircraft will be identified immediately after departure ( I said "identified" not told "radar contact" which comes after identification) then a heading may be specified BY THE RADAR CONTROLLER who controls the airspace. And if it will be specified then there is proper phraseology for that.
If the airspace into which the IFR flight is being launched is radar controlled AND the aircraft WILL NOT be immediately identified after departure AND a heading is necessary to be flown immediately after departure then the phraseology will be...
"WHEN ENTERING CONTROLLED AIRSPACE (instruction), FLY HEADING (degrees) UNTIL REACHING (altitude, point, or fix) BEFORE
PROCEEDING ON COURSE."
If the airspace is not radar controlled or the aircraft will have to depart via non-radar procedures then the VFR tower will give some non-radar-ish instruction (again, by the direction of the controlling facility) to depart using non-radar routing, ie, "after departure proceed direct ALPHA VOR then proceed on course, cleared for takeoff".
Or, the VFR tower will instruct the aircraft to proceed on course into a radar environment.
There is really only these four possibilities and the four standard phraseological methods.
Regarding VFR towers and IFR departures...they do NOTHING without the consent and direction of the controller who controls the airspace into which they are launching the aircraft either directly or by letter of agreement with the radar facility. Really the only IFR separation responsibility given to a VFR tower (FAA as opposed to contract) is the 2 increasing to 3 departure rule and the 15 degree (radar) or two or three non-radar departure rules. And even those are ALLOWED by permission by the facility controlling the airspace into which the aircraft are being launced by LOA. So there will be no freelance phraseology necessary to deal with IFR aircraft.
VFR departures that will receive radar service are treated the same, generally, and with the consent and direction of the radar facility into which the plane is being launched.
VFR departures that will not receive radar service may be handled at the discretion of the tower but, still, by the use of standard phraseology and .65 methods. There is no justification or excuse or legal necessity to be sloppy in those circumstances.
All controllers as well as pilots pick up bad habits. A controller picks up some non-standard way of saying something because it sounds cool or folksy or "I'm good enough I don't need to follow the rules" mentality. Then he teaches that to his trainee who teaches his trainee who teaches his trainee. Then when these controllers move to other facilities they infect that facility with the poor example and before long now the virus has spread to other facilities and regions and new trainees.
This is why, we as instructors need to teach the correct FAA way of doing things in order to stop the mutations from continuing generationally, whether we teach air traffic control or piloting. We must carefully differentiate between teaching standard basics and "our way" of doing things. I always make a point of making sure that when I teach MY way about something that they understand that it is MY method or interpretation.
One thing I have learned in almost 40 years of doing this is that almost nothing requires "interpretation", which is usually a vehicle used to defend one's personal taste or agenda. Most of the rules are clear and understandable if one studies the rule.
tex