My limited knowledge and understanding leaves me with some questions and observations here.
It appears there are 2 separate and distinct albeit conjoined issues that are being addressed here.
1. Inrush current. Measured in amps.
2. Voltage regulation. Measured in volts.
As I understand it, inrush current is a phenomenon observed when a transformer or a capacitor is initially energized. When a transformer is energized, it can draw a large amount of current, perhaps several times its rated capacity until its core is magnetized and it operating resistance is stabilized. A capacitor does similar until it is fully charged.
This inrush current is typically allowed for in the design of the transformer and all downstream components, otherwise, there would be large scale component failures. The primary concern of current inrush is not downstream components but rather upstream components. If the supply for the device is not capable of carrying the large amount of current required instantaneously when the device is brought on line problems can occur. 1) a breaker or fuse can trip or blow, 2) a conductor can burn or overheat, 3) the generation source can be overloaded. A combination of these events may occur, not in the particular order listed.
A breaker tripping or fuse blowing is pretty typical and obvious. Many breaker manufacturers allow for short term transients and some even have adjustments for thresholds. A slow-blow fuse is a primitive time delay overcurrent protection.
Another symptom of inrush current is an initial voltage sag followed by a voltage surge. As a switch allows electrons to flow into the transformer or capacitor, the initial low resistance creates a voltage sag. As the transformer and capacitor reach operating condition, resistance is restored and the inrush current comes to a halt with a short voltage rise resulting before the circuit becomes stable as the conga line of electrons that has been rushing to fill the bar suddenly gets the door slammed shut and they all plow into each other.
Protection from these events must be addressed from both current and voltage perspectives if your goal is to extend the life of equipment. As Sluckey indicated, current inrush is most often addressed by use of Thermistors. Thermistors however are not voltage regulators and wil do nothing to prevent sag or surge of voltage in the circuit. To address Voltage sag, a capacitor or battery storage bank is typically used, and to protect from a surge a MOV is typically the most cost effective solution. A well designed and well regulated power supply typically incorporates a Breaker or fuse, a transformer or voltage regulator, a capacitor, and an MOV. In some cases to maximize protection, MOV's are installed both before and after the transformer.
Unless you are located in a third world country or California, where the grid is unreliable and dynamic, these concerns are probably not something you need to lose sleep over when applied to tube amplifiers. One of the beauties of Tube gear is their relatively large tolerance of dirty power and reasonable voltage swing.
I would liken this to an first time expectant mother. If a mother has never birthed a child before, she will think it requires a great amount of diligence and preparation, every last detail has to be planned and a lot of books are read, and doo dads purchased to create the theoretically perfect nest. Diet must be perfect, vitamins taken, doctors visited, birthing classes taken, and baby showers held. Despite all the hand wringing and consternation exhibited by first time mothers, birthing a child is something that happens all the time, most often with little fanfare, often in the most primitive and less than elegant manner and there is little empirical evidence to suggest that a well planned sanitary hospital birth is in some way superior to a birth in the backseat of a car when it comes to the long term effect on the child. General guidelines are sufficient, don't drink, smoke, or do drugs while pregnant, and don't engage in risky behavior before and chances are things will turn out just fine.
If you want that extra peace of mind that having the best OB/GYN care, a sanitary hospital bed and a staff on onlooking spectators can bring, then there is no compelling reason not to spend the extra money but it is still no guarantee that nature will not decide on an alternative course.
Most 3rd or fourth time mothers will likely tell you they went way overboard on their first pregnancy and to save your money for more important things.