Here are some graphs I slapped together with matplotlib:
https://imgur.com/a/VSPKtIeBoth graphs are 200mg per week. Green is dosed at once every 7 days, while the blue is broken into 7 smaller doses per week. (I haven't included axis and such, because it's really just the shape I'm trying to highlight)
As you can see, more frequent dosing results in steadier levels.
When administering your testosterone once per week, you will have to make one of a couple trade offs:
1) Dose high enough that you are above the level you want to be by the end of the week. This avoids the "crash" you mention, which will consist of both low-testosterone (low-libido, fatigue, etc) and low-estrogen[1] (joint pain, etc) side effects. Dosing higher means you shift the whole graph up, and you will be at supra-physiological levels of testosterone and estrogen, and the high estrogen side effects are no fun: nipple sensitivity, emotional fluctuations (think crying at the sight of puppy pictures), gynecomastia (development of breast tissue), horrible back acne, etc.
2) Dose on the lower side to avoid avoid high testosterone/estrogen side effects. This shifts the whole graph down, and now you're below where you want to be by the end of the week, and you now feel more like you did before you started TRT.
3) Somewhere between the above two options, and add an aromatase inhibitor (like anastrozole) to minimize high estrogen levels. You'll still have excessively high testosterone though... and you'd really be better off avoiding the high testosterone peaks instead of adding another drug to the mix.
I used to go into a clinic once a week for an intramuscular injection of testosterone cypionate. In order to not feel like shit the last two or three days of the week, I had to up my dose such that my back broke out in a constellation of acne, and probably negatively impacted my health in other more meaningful (but less obvious) ways.
Now I inject testosterone propionate every night. I managed to lower my dose so that I'm always hovering right around where I want to be, instead of bouncing all over the place.
That's another benefit of increased injection frequency: you can lower the total amount of testosterone injected per week while staying within therapeutic range.
1: Your body produces estrogen by aromatising testosterone. More testosterone and/or more aromatase -> higher estrogen. Less testosterone and/or aromatase -> lower estrogen.