You could, and for about a fortnight it would be faster. Then it would quietly cap everything you do afterwards.
The argument is not cultural authenticity or discipline. It is that the tone is in the spelling and it is not in the romanisation.
What romanisation loses
The system on Thai road signs, RTGS, marks neither tone nor vowel length. It writes เขา (he) and ขาว (white) and ข้าว (rice) with overlapping spellings, and gives you no way to recover which is which.
Systems that do mark tone (Paiboon and its relatives) are better, but every one of them is a private convention. There are several, they disagree, and none is used on anything you will encounter in Thailand.
Thai spelling, by contrast, encodes the tone completely. Four facts determine it with almost no exceptions: consonant class, live or dead, vowel length, tone mark. That is what this app's engine computes, and it can only do so because the script is there.
- ขาวkʰǎːw
white
- ข่าวkʰàːw
news
- ข้าวkʰâːw
rice
one mark apart; romanisation flattens the difference
The practical case
You live in Thailand. Menus, signs, bus destinations, 7-Eleven labels and the name of your own street are in Thai script and nothing else. Romanisation buys you no access to any of it.
And there is a compounding effect: a word you meet in script carries its tone with it every time you see it. A word you meet in romanisation has to have its tone attached separately and remembered by brute force, which is exactly the memorisation you said you wanted less of.
The honest cost
Three to four weeks before reading feels anything but laborious, and a fortnight of feeling slower than you would with romanisation.
The trade is that transcription is training wheels you have to take off later, and taking them off after six months of dependence is much harder than never fitting them. This app therefore shows the transcription at first and removes it word by word as you demonstrate you no longer need it.